A118370 Divisorial primes: Primes p such that p = 1 + Product_{d|n} d for some n (ordered by n).

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

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-François 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