login
The OEIS is supported by the many generous donors to the OEIS Foundation.
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
Search: a177820 -id:a177820
Displaying 1-8 of 8 results found.
page 1
     Sort: relevance | references | number | modified | created      Format: long | short | data
A127263
Numbers k such that k^3 divides 2^(k^2)+1.
+10
19
1, 3, 57, 32547, 9961491, 297381939, 1338104811, 3942759027, 5688011361, 8920514307, 9146532873, 40253706489, 243640690617, 764039295291, 1127102902923, 1556475424971, 2251315404417, 3005607686883, 5222670270483
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
If k belongs to this sequence, then so does (2^(k^2)+1)/k^2.
From Alexander Adamchuk, May 14 2010: (Start)
3 divides a(n) for n>1.
19 divides a(n) for n>2. (End)
LINKS
Table of n, a(n) for n=1..19.
ArtOfProblemSolving forum, n^3 | (2^{n^2}+1)
MATHEMATICA
Select[Range[100000], Divisible[2^(#^2) + 1, #^3] &] (* Robert Price, Mar 23 2020 *)
CROSSREFS
Cf. A006521, A093546, A093665, A136372, A128677.
Cf. A128678, A128679, A128680, A128681, A128682, A128683, A128684, A128685, A177813, A177814, A177816, A177817, A177818, A177819, A177820.
KEYWORD
nonn
AUTHOR
Max Alekseyev, Mar 27 2007, Mar 29 2007, Apr 18 2007
EXTENSIONS
a(7) from Ryan Propper, Jan 01 2008
a(8)-a(19) from Max Alekseyev, May 14 2010
STATUS
approved
A177813
Numbers k such that k^3 divides 13^(k^2) + 1.
+10
11
1, 7, 203, 11977, 154553, 353423, 3049963, 4482037, 5192537, 7170569, 9904979, 20851957, 33461911, 35852033, 69262991, 88448927, 160274303, 264440183, 306359683, 381231473, 423063571, 978466699, 1974252749, 2115269947, 4647954787, 5218486693, 6824905927, 7803226417, 9040206917, 10041409007, 11055712717, 12483960629, 17244568439, 47773414171, 57280493557, 57729535241, 58257187051, 62418389453, 67340133077
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
7 divides a(n) for n > 1.
Prime factors of a(n) in the order of their appearance are {7, 29, 59, 22079, 1741, 435709, 25579, 35323, 827, 164837, 176611, 5783, 435709, 22896329, 54461639, 4820033, ...}. - Alexander Adamchuk, May 16 2010
LINKS
Table of n, a(n) for n=1..39.
CROSSREFS
Cf. A127263 (k^3 divides 2^(k^2) + 1).
Cf. A128678, A128679, A128680, A128681, A128682, A128683, A128684, A128685.
Cf. A177813, A177814, A177816, A177817, A177818, A177819, A177820.
Cf. A128677 (least k > p such that (k*p)^3 divides (p-1)^(k*p)^2+1, where p = prime(n) > 2).
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, May 14 2010
EXTENSIONS
Corrected and extended by Max Alekseyev, May 16 2010
a(8) = 4482037 (suggested by Max Alekseyev) missing in original sequence inserted by Alexander Adamchuk, May 16 2010
More terms from Max Alekseyev, Feb 14 2012
STATUS
approved
A177814
Numbers k such that k^3 divides 14^(k^2) + 1.
+10
11
1, 3, 5, 15, 57, 183, 285, 355, 505, 915, 1065, 1515, 2005, 2265, 3477, 6015, 10887, 12165, 17385, 20005, 20235, 27015, 28785, 35855, 43035, 54435, 60015, 64965, 92415, 107565, 114285, 134139, 138165, 142355, 160815, 201995, 202505, 228765
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Table of n, a(n) for n=1..38.
CROSSREFS
Cf. A127263 (k^3 divides 2^(k^2) + 1).
Cf. A128678, A128679, A128680, A128681, A128682, A128683, A128684, A128685.
Cf. A177813, A177814, A177816, A177817, A177818, A177819, A177820.
Cf. A128677 (least k > p such that (k*p)^3 divides (p-1)^(k*p)^2+1, where p = prime(n) > 2).
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, May 14 2010
STATUS
approved
A177816
Numbers k such that k^3 divides 16^(k^2) + 1.
+10
9
1, 17, 707489, 5030929, 6029713, 209372172193, 250938565921, 1413292053713, 1784415176081, 24025953593297, 48948914347889, 1423524187400657, 5817190224008753, 49446116858851553, 74262006382962977
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
17 divides a(n) for n > 1.
LINKS
Table of n, a(n) for n=1..15.
CROSSREFS
Cf. A127263 k^3 divides 2^(k^2) + 1).
Cf. A128678, A128679, A128680, A128681, A128682, A128683, A128684, A128685.
Cf. A177813, A177814, A177816, A177817, A177818, A177819, A177820.
Cf. A128677 (least k > p such that (k*p)^3 divides (p-1)^(k*p)^2+1, where p = prime(n) > 2).
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, May 14 2010
EXTENSIONS
Terms a(6) onward from Max Alekseyev, May 16 2010
STATUS
approved
A177817
Numbers k such that k^3 divides 17^(k^2) + 1.
+10
9
1, 3, 9, 21, 39, 63, 117, 273, 819, 1467, 2067, 3081, 4269, 6201, 7299, 9243, 10269, 12807, 14469, 16959, 19071, 20421, 21567, 23877, 29883, 43407, 48711, 50877, 51093, 55497, 64701, 89649, 94887, 118713, 133497, 142947, 146133, 149331
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
3 divides a(n) for n > 1.
LINKS
Table of n, a(n) for n=1..38.
CROSSREFS
Cf. A127263 (k^3 divides 2^(k^2) + 1).
Cf. A128678, A128679, A128680, A128681, A128682, A128683, A128684, A128685.
Cf. A177813, A177814, A177816, A177817, A177818, A177819, A177820.
Cf. A128677 (least k > p such that (k*p)^3 divides (p-1)^(k*p)^2+1, where p = prime(n) > 2).
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, May 14 2010
STATUS
approved
A177818
Numbers k such that k^3 divides 18^(k^2) + 1.
+10
9
1, 19, 397841, 1152331, 3566699, 24128658809, 74683110361, 216316727651, 1339092172657, 7967201553697
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
19 divides a(n) for n > 1.
LINKS
Table of n, a(n) for n=1..10.
CROSSREFS
Cf. A127263 (k^3 divides 2^(k^2) + 1).
Cf. A128678, A128679, A128680, A128681, A128682, A128683, A128684, A128685.
Cf. A177813, A177814, A177816, A177817, A177818, A177819, A177820.
Cf. A128677 (least k > p such that (k*p)^3 divides (p-1)^(k*p)^2+1, where p = prime(n) > 2).
KEYWORD
more,nonn
AUTHOR
Alexander Adamchuk, May 14 2010
EXTENSIONS
a(6)-a(10) from Max Alekseyev, May 16 2010
STATUS
approved
A177819
Numbers k such that k^3 divides 19^(k^2) + 1.
+10
9
1, 5, 55, 1265, 11255, 59455, 123805, 395755, 635255, 874115, 1028555, 1456015, 2847515, 3201715, 3841805, 4353305, 6655055, 6987805, 13443155, 16825765, 23656765, 36370015, 41083405, 66919765, 68432705, 100126015, 123012395
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
5 divides a(n) for n > 1.
LINKS
Table of n, a(n) for n=1..27.
MATHEMATICA
Select[Range[123020000], PowerMod[19, #^2, #^3]==#^3-1&] (* Harvey P. Dale, May 20 2021 *)
CROSSREFS
Cf. A127263 (k^3 divides 2^(k^2) + 1).
Cf. A128678, A128679, A128680, A128681, A128682, A128683, A128684, A128685.
Cf. A177813, A177814, A177816, A177817, A177818, A177819, A177820.
Cf. A128677 (least k > p such that (k*p)^3 divides (p-1)^(k*p)^2+1, where p = prime(n) > 2).
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, May 14 2010
EXTENSIONS
More terms from Max Alekseyev, May 16 2010
STATUS
approved
A136372
Prime factors of terms of A127263.
+10
3
3, 19, 571, 9137, 41113, 174763, 274081, 1236787, 7485811, 23474953, 34630009, 47822393, 69171211, 92346689, 160465489
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
From Alexander Adamchuk, May 14 2010: (Start)
3 divides A127263(n) for n > 1.
19 divides A127263(n) for n > 2. (End)
LINKS
Table of n, a(n) for n=1..15.
EXAMPLE
A127263(1) = 1,
A127263(2) = 3,
A127263(3) = 57 = 3*19,
A127263(4) = 32547 = 3*19*571,
A127263(5) = 9961491 = 3*19*174763,
A127263(6) = 297381939 = 3*19*571*9137.
CROSSREFS
Cf. A127263, A128677, A128678, A128679, A128680, A128681, A128682, A128683, A128684, A128685, A136373.
Cf. A177813, A177814, A177816, A177817, A177818, A177819, A177820. - Alexander Adamchuk, May 14 2010
KEYWORD
nonn,hard,more
AUTHOR
Alexander Adamchuk, Dec 27 2007
EXTENSIONS
Edited and extended by Max Alekseyev, May 14 2010
STATUS
approved
page 1

Search completed in 0.006 seconds

Lookup Welcome Wiki Register Music Plot 2 Demos Index WebCam Contribute Format Style Sheet Transforms Superseeker Recents
The OEIS Community
Maintained by The OEIS Foundation Inc.
Last modified September 30 21:24 EDT 2024. Contains 376365 sequences.
License Agreements, Terms of Use, Privacy Policy