A137258 Primes p that satisfy s-t < 0 where s = sigma(2*p+1) mod phi(p) and t = sigma(2*p+1) mod p.

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

Offset

1,1

Comments

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

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

a(15) > 2*10^9. - Donovan Johnson, Feb 15 2013

Links

Table of n, a(n) for n=1..14.

Mathematica

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 *)

Prog

(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 */

Crossrefs

Sequence in context: A125739 A219461 A122853 * A053341 A331894 A357234

Adjacent sequences: A137255 A137256 A137257 * A137259 A137260 A137261

Keyword

nonn,more

Author

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

Extensions

a(10)-a(12) added by R. J. Mathar, May 23 2008

a(13)-a(14) from Donovan Johnson, Feb 15 2013

Status

approved