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Divisorial primes: Primes p such that p = 1 + Product_{d|n} d for some n (ordered by n).
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%I #13 Jan 03 2021 22:55:50

%S 2,3,37,101,197,331777,677,8503057,9834497,5477,59969537,8837,17957,

%T 21317,562448657,916636177,42437,3208542737,3782742017,5006411537,

%U 7676563457,98597,106277,11574317057,19565295377,416806419029812551937,148997,34188010001,38167092497

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

%C 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).).

%H Amiram Eldar, <a href="/A118370/b118370.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%t 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 *)

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

%Y Cf. A118369, A007955.

%Y Cf. A014545, A088332.

%Y Cf. A258455 (sorted).

%K nonn

%O 1,1

%A _Rick L. Shepherd_, Apr 25 2006