A259973 - OEIS

A259973

Numbers n such that sigma(n) + product of divisors of n is prime.

1, 2, 3, 5, 8, 11, 23, 27, 29, 32, 41, 50, 53, 57, 83, 85, 89, 111, 113, 128, 131, 161, 173, 179, 191, 215, 233, 237, 239, 245, 251, 265, 275, 281, 293, 319, 355, 359, 365, 391, 413, 419, 431, 437, 443, 453, 481, 485, 491, 493, 505, 509, 511, 535, 589, 593, 603

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OFFSET

1,2

COMMENTS

If p is prime, then (sigma(p) + product of divisors of p) = 2*p+1. So the subsequence of primes gives the Sophie Germain primes: A005384. - Michel Marcus, Jul 16 2015

LINKS

K. D. Bajpai, Table of n, a(n) for n = 1..10000

EXAMPLE

a(5) = 8; divisors(8) = {1,2,4,8}; sum = 1+2+4+8 = 15; product = 1*2*4*8 = 64; 15 + 64 = 79, which is prime.

a(8) = 27; divisors(27) = {1,3,9,27}; sum = 1+3+9+27 = 40; product = 1*3*9*27 = 729; 40+729 = 769, which is prime.

MATHEMATICA

Select[Range[2000], PrimeQ[DivisorSigma[1, #] + Times@@Divisors[#]] &]

PROG

(Magma) [n: n in[1..1000] | IsPrime(&*Divisors(n) + SumOfDivisors(n))];

(PARI) for(n=1, 1000, d=divisors(n); k=sigma(n) + prod(i=1, #d, d[i]); if(isprime(k), print1(n, ", ")));

CROSSREFS

Cf. A000203, A007955, A005384, A065512, A118369.