A137258 - OEIS

%I #8 Nov 16 2024 18:55:11

%S 3,5,7,17,19,139,157,577,1201,27361,530401,2513281,7183201,407817217

%N Primes p that satisfy s-t < 0 where s = sigma(2*p+1) mod phi(p) and t = sigma(2*p+1) mod p.

%C The function sigma(n) is the sum of positive divisors function and the function phi(n) is the Euler totient function.

%C The positive values of s-t for primes p<2000 are 0, 2, 3, 4.

%C a(15) > 2*10^9. - _Donovan Johnson_, Feb 15 2013

%t ds1Q[p_]:=With[{c=DivisorSigma[1,2p+1]},Mod[c,EulerPhi[p]]-Mod[c,p]<0]; Select[Prime[Range[500000]],ds1Q] (* The program generates the first 13 terms of the sequence. *) (* _Harvey P. Dale_, Nov 16 2024 *)

%o (PARI) p=1; for(i=1, 10^9, p=nextprime(p+1); s=sigma(2*p+1); if(s%(p-1)<s%p, print(p))) /* _Donovan Johnson_, Feb 15 2013 */

%K nonn,more,changed

%O 1,1

%A Juan Lopez Gonzalez (juan.lopezg(AT)estudiante.uam.es), Apr 25 2008

%E a(10)-a(12) added by _R. J. Mathar_, May 23 2008

%E a(13)-a(14) from _Donovan Johnson_, Feb 15 2013