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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.
0
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
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
KEYWORD
nonn,more,changed
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