The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A171664

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A171664

Numbers k such that (Product_{d|k} d) - k - 1 and (Product_{d|k} d) + k + 1 are primes.
(history; published version)

#10 by Harvey P. Dale at Mon Aug 30 12:15:28 EDT 2021

STATUS

editing

approved

#9 by Harvey P. Dale at Mon Aug 30 12:15:26 EDT 2021

MATHEMATICA

Select[Range[3200], AllTrue[Times@@Divisors[#]+{(#+1), (-#-1)}, PrimeQ]&] (* Harvey P. Dale, Aug 30 2021 *)

STATUS

approved

editing

#8 by Alois P. Heinz at Sun Jan 03 22:36:45 EST 2021

STATUS

proposed

approved

#7 by Jon E. Schoenfield at Sun Jan 03 22:35:44 EST 2021

STATUS

editing

proposed

Discussion

Sun Jan 03

22:36

Alois P. Heinz: perfect, thanks!

#6 by Jon E. Schoenfield at Sun Jan 03 22:35:18 EST 2021

EXAMPLE

Divisors of 6: 1,2,3,6. As 6*3*2*1 = 36, 36 - 6 - 1 = 29 is prime, 6*3*2*1 = and 36 + 6 + 1 = 43 is prime, 6 is a term.

Discussion

Sun Jan 03

22:35

Jon E. Schoenfield: Good catch!  How's this?

#5 by Alois P. Heinz at Sun Jan 03 21:38:47 EST 2021

STATUS

proposed

editing

#4 by Jon E. Schoenfield at Sun Jan 03 12:11:42 EST 2021

STATUS

editing

proposed

Discussion

Sun Jan 03

21:24

Alois P. Heinz: name is ok.  But example is not ok.   6*3*2*1 is NOT = 29 and 6*3*2*1 is NOT = 43.

#3 by Jon E. Schoenfield at Sun Jan 03 12:10:41 EST 2021

NAME

Numbers n k such that prod_(Product_{d|nk} d) -n k - 1 and (Product_{d|k} d) +n k + 1 are primes.

EXAMPLE

Divisors of 6: 1,2,3,6. As 6*3*2*1 = 36-6-1 = 29 is prime, 6*3*2*1 = 36+6+1 = 43 is prime, 6 is a term.

CROSSREFS

Cf. A118369.

STATUS

approved

editing

Discussion

Sun Jan 03

12:11

Jon E. Schoenfield: Edits to Name okay?  Or maybe "Numbers k such that both P-k-1 and P+k+1 are primes, where P is the product of the divisors of k."?

#2 by Russ Cox at Sat Mar 31 12:38:28 EDT 2012

AUTHOR

_Vladimir Joseph Stephan Orlovsky (4vladimir(AT)gmail.com), _, Dec 14 2009

Discussion

Sat Mar 31

12:38

OEIS Server: https://oeis.org/edit/global/876

#1 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

NAME

Numbers n such that prod_{d|n} d-n-1 and d+n+1 are primes.

DATA

4, 6, 9, 14, 18, 21, 27, 57, 69, 77, 141, 155, 161, 194, 261, 381, 428, 551, 579, 620, 626, 671, 672, 704, 720, 755, 1007, 1349, 1506, 1529, 1611, 1659, 1707, 1710, 1814, 1982, 1986, 1994, 2036, 2037, 2157, 2429, 2651, 2714, 2771, 2783, 2966, 3039, 3044, 3101

OFFSET

1,1

EXAMPLE

Divisors of 6: 1,2,3,6. As 6*3*2*1=36-6-1=29 is prime, 6*3*2*1=36+6+1=43 is prime, 6 is a term.

MATHEMATICA

f[n_]:=PrimeQ[Times@@Divisors[n]-n-1]&&PrimeQ[Times@@Divisors[n]+n+1]; lst={}; Do[If[f[n], AppendTo[lst, n]], {n, 7!}]; lst

CROSSREFS

Cf. A118369

KEYWORD

nonn

AUTHOR

Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 14 2009

STATUS

approved