A249410 Primes p such that sigma(p-1) is odd.

2, 3, 5, 17, 19, 37, 73, 101, 163, 197, 257, 401, 577, 677, 883, 1153, 1297, 1459, 1601, 1801, 2179, 2593, 2917, 3137, 3529, 4051, 4357, 5477, 7057, 8101, 8713, 8837, 10369, 11251, 12101, 13457, 14401, 15139, 15377, 15877, 16901, 17299, 17957, 18433, 19603

Offset

1,1

Comments

Subsequence of A058501.

Union of A002496 and A090698. - Ivan Neretin, Dec 04 2018

Except for the terms 2 and 3, union of the primes of the form 4*k^2 + 1 and the primes of the form 18*k^2 + 1. - Jianing Song, Nov 14 2021

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

2 is in this sequence because 2 is prime and sigma(2-1) = 1 is odd.

Mathematica

Select[Range[20000], PrimeQ[#] && OddQ[DivisorSigma[1, #-1]] &] (* Amiram Eldar, Dec 04 2018 *)

Prog

(PARI) lista(nn) = {forprime(p=2, nn, if (sigma(p-1) % 2, print1(p, ", ")); ); } \\ Michel Marcus, Oct 30 2014
(PARI) list(lim)=my(v=List([2]), t); forstep(n=2, sqrt(lim), 2, if(isprime(t=n^2+1), listput(v, t))); for(n=1, sqrtint(lim\2), if(isprime(t=2*n^2+1), listput(v, t))); Set(v) \\ Charles R Greathouse IV, Nov 04 2014
(GAP) Filtered(Filtered([1..25000], i->IsPrime(i)), p->IsOddInt(Sigma(p-1))); # Muniru A Asiru, Dec 05 2018

Crossrefs

Cf. A000203, A058501, A090698.

Sequence in context: A290043 A058501 A215356 * A119405 A032733 A111632

Adjacent sequences: A249407 A249408 A249409 * A249411 A249412 A249413

Keyword

nonn

Author

Juri-Stepan Gerasimov, Oct 27 2014

Extensions

More terms from Michel Marcus, Oct 30 2014

Status

approved