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

Author

Rick L. Shepherd, Apr 25 2006

Keywords

• nonn

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).).

Examples

			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.
		

Links

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

Crossrefs

Cf. A118369, A007955.

Cf. A014545, A088332.

Cf. A258455 (sorted).

Programs

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 *)

PARI

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