A164319 Primes p such that the sum of divisors of p+1 is larger than 2*p.

3, 5, 7, 11, 17, 19, 23, 29, 31, 41, 47, 53, 59, 71, 79, 83, 89, 101, 103, 107, 113, 127, 131, 137, 139, 149, 167, 173, 179, 191, 197, 199, 223, 227, 233, 239, 251, 257, 263, 269, 271, 281, 293, 307, 311, 317, 347, 349, 353, 359, 367, 379, 383, 389, 401, 419

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Aug 12 2009

Keywords

• nonn

Comments

For a subset of these, namely p=179, 239, 359, 419, etc, sigma(p+1) is even larger than 3*p.

Examples

			For p=3, the sum of divisors of p+1 is A000203(4)=7 > 2*3, so p=3 is in the sequence.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A008333, A085498, A164318.

Programs

Mathematica

f[n_]:=Plus@@Divisors[n]; lst={};Do[p=Prime[n];If[f[p+1]>2*p,AppendTo[lst, p]],{n,6!}];lst
Select[Prime[Range[100]], DivisorSigma[1, # + 1] > 2 # &] (* G. C. Greubel, Sep 13 2017 *)

PARI

lista(nn) = forprime(p=2, nn, if (sigma(p+1) > 2*p, print1(p, ", "))); \\ Michel Marcus, Sep 13 2017

Extensions

Edited by R. J. Mathar, Aug 21 2009