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A118370 Divisorial primes: Primes p such that p = 1 + Product_{d|n} d for some n (ordered by n). 4
2, 3, 37, 101, 197, 331777, 677, 8503057, 9834497, 5477, 59969537, 8837, 17957, 21317, 562448657, 916636177, 42437, 3208542737, 3782742017, 5006411537, 7676563457, 98597, 106277, 11574317057, 19565295377, 416806419029812551937, 148997, 34188010001, 38167092497 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A118369 for the corresponding n. These are primes in the sequence 1 + A007955. (The suggested name "divisorial prime" is obviously analogous to that of factorial primes (A088332) and primorial primes (A014545).).

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

The prime 37 is a(3) as there exists a number, A118369(3)=6, such that 37 = 6*3*2*1 + 1, where {1,2,3,6} are all the positive divisors of 6.

MATHEMATICA

Reap[For[n = 1, n <= 500, n++, p = Times @@ Divisors[n]; If[PrimeQ[p+1], Sow[p+1]]]][[2, 1]] (* Jean-Fran├žois Alcover, Oct 07 2016 *)

PROG

(PARI) for(n=1, 2500, s=1; fordiv(n, d, s=s*d); if(isprime(s+1), print1(s+1, ", ")))

CROSSREFS

Cf. A118369, A007955.

Cf. A014545, A088332.

Cf. A258455 (sorted).

Sequence in context: A109748 A062459 A258455 * A189027 A061576 A221055

Adjacent sequences:  A118367 A118368 A118369 * A118371 A118372 A118373

KEYWORD

nonn

AUTHOR

Rick L. Shepherd, Apr 25 2006

STATUS

approved

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Last modified October 3 06:21 EDT 2022. Contains 357230 sequences. (Running on oeis4.)