A164319 - OEIS

%I #8 Sep 14 2017 04:12:43

%S 3,5,7,11,17,19,23,29,31,41,47,53,59,71,79,83,89,101,103,107,113,127,

%T 131,137,139,149,167,173,179,191,197,199,223,227,233,239,251,257,263,

%U 269,271,281,293,307,311,317,347,349,353,359,367,379,383,389,401,419

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

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

%H G. C. Greubel, <a href="/A164319/b164319.txt">Table of n, a(n) for n = 1..5000</a>

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

%t f[n_]:=Plus@@Divisors[n]; lst={};Do[p=Prime[n];If[f[p+1]>2*p,AppendTo[lst, p]],{n,6!}];lst

%t Select[Prime[Range[100]], DivisorSigma[1, # + 1] > 2 # &] (* _G. C. Greubel_, Sep 13 2017 *)

%o (PARI) lista(nn) = forprime(p=2, nn, if (sigma(p+1) > 2*p, print1(p, ", "))); \\ _Michel Marcus_, Sep 13 2017

%Y Cf. A008333, A085498, A164318.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Aug 12 2009

%E Edited by _R. J. Mathar_, Aug 21 2009