A118369 Numbers k such that 1 + Product_{d|k} d is prime.

1, 2, 6, 10, 14, 24, 26, 54, 56, 74, 88, 94, 134, 146, 154, 174, 206, 238, 248, 266, 296, 314, 326, 328, 374, 378, 386, 430, 442, 466, 472, 488, 494, 498, 510, 568, 582, 584, 634, 674, 680, 710, 730, 742, 786, 856, 874, 894, 918, 962, 986, 1038, 1094, 1174

Offset: 1

Author

Rick L. Shepherd, Apr 25 2006

Keywords

• nonn

Comments

See A118370 for the corresponding primes, 'divisorial primes'.

Examples

			The (positive) divisors of 6 are 1,2,3,6. As 6*3*2*1 + 1 = 37 is prime, 6 is a term.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A118370, A007955.

Programs

Mathematica

f[n_]:=PrimeQ[Times@@Divisors[n]+1]; lst={};Do[If[f[n],AppendTo[lst,n]],{n,7!}];lst (* Vladimir Joseph Stephan Orlovsky, Dec 14 2009 *)

PARI

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