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A258600
a(n) is the index m such that A036966(m) = prime(n)^3.
9
2, 4, 8, 13, 23, 29, 39, 45, 57, 75, 81, 99, 110, 117, 130, 149, 169, 176, 197, 209, 212, 236, 250, 270, 295, 309, 317, 328, 337, 354, 399, 414, 436, 445, 477, 483, 506, 529, 541, 563, 585, 591, 631, 635, 654, 657, 697, 747, 758, 765, 781, 803, 809, 845, 864
OFFSET
1,1
LINKS
FORMULA
A036966(a(n)) = A030078(n) = prime(n)^3.
A036966(m) mod prime(n) > 0 for m < a(n).
Also smallest number m such that A258568(m) = prime(n):
A258568(a(n)) = A000040(n) and A258568(m) != A000040(n) for m < a(n).
EXAMPLE
. n | p | a(n) | A036966(a(n)) = A030078(n) = p^3
. ----+----+-------+---------------------------------
. 1 | 2 | 2 | 8
. 2 | 3 | 4 | 27
. 3 | 5 | 8 | 125
. 4 | 7 | 13 | 343
. 5 | 11 | 23 | 1331
. 6 | 13 | 29 | 2197
. 7 | 17 | 39 | 4913
. 8 | 19 | 45 | 6859
. 9 | 23 | 57 | 12167
. 10 | 29 | 75 | 24389
. 11 | 31 | 81 | 29791
. 12 | 37 | 99 | 50653
. 13 | 41 | 110 | 68921
. 14 | 43 | 117 | 79507
. 15 | 47 | 130 | 103823
. 16 | 53 | 149 | 148877
. 17 | 59 | 169 | 205379
. 18 | 61 | 176 | 226981
. 19 | 67 | 197 | 300763
. 20 | 71 | 209 | 357911
. 21 | 73 | 212 | 389017
. 22 | 79 | 236 | 493039
. 23 | 83 | 250 | 571787
. 24 | 89 | 270 | 704969
. 25 | 97 | 295 | 912673 .
MATHEMATICA
With[{m = 60}, c = Select[Range[Prime[m]^3], Min[FactorInteger[#][[;; , 2]]] > 2 &]; 1 + Flatten[FirstPosition[c, #] & /@ (Prime[Range[m]]^3)]] (* Amiram Eldar, Feb 07 2023 *)
PROG
(Haskell)
import Data.List (elemIndex); import Data.Maybe (fromJust)
a258600 = (+ 1) . fromJust . (`elemIndex` a258568_list) . a000040
(Python)
from math import gcd
from sympy import prime, integer_nthroot, factorint
def A258600(n):
c, m = 0, prime(n)**3
for w in range(1, integer_nthroot(m, 5)[0]+1):
if all(d<=1 for d in factorint(w).values()):
for y in range(1, integer_nthroot(z:=m//w**5, 4)[0]+1):
if gcd(w, y)==1 and all(d<=1 for d in factorint(y).values()):
c += integer_nthroot(z//y**4, 3)[0]
return c # Chai Wah Wu, Sep 10 2024
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jun 06 2015
EXTENSIONS
a(11)-a(55) and example corrected by Amiram Eldar, Feb 07 2023
STATUS
approved