A189411 Odd primes p such that sigma(p)/2 is a power of an odd prime.

5, 13, 17, 37, 53, 61, 73, 97, 157, 193, 241, 277, 313, 337, 397, 421, 457, 541, 577, 613, 661, 673, 733, 757, 877, 997, 1093, 1153, 1201, 1213, 1237, 1249, 1321, 1381, 1453, 1621, 1657, 1753, 1873, 1933, 1993, 2017, 2137, 2341, 2473

Offset

1,1

Comments

Equivalently odd prime numbers p in increasing order such that p is of the form 2q^h - 1 for some odd prime number q and some positive integer h >= 1.

Links

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

Example

For n = 5 one has a(5) = 53 since a(1) = 5, a(2) = 13, a(3) = 17, a(4) = 37 and 53 = 2 * 3^3 - 1 is the smallest prime p > 37 of the form p = 2 * q^h - 1, with q an odd prime and h >= 1 a positive integer.

Maple

with(numtheory):
a:= proc(n) option remember; local l, p;
      p:= `if`(n=1, 2, a(n-1));
      do p:= nextprime(p);
         l:= ifactors(sigma(p)/2)[2];
         if nops(l)=1 and l[1][1]<>2 then break fi
      od; p
    end:
seq(a(n), n=1..60);  # Alois P. Heinz, Apr 22 2011

Mathematica

selQ[p_] := Module[{s, f}, s = DivisorSigma[1, p]/2; f = FactorInteger[s]; Length[f] == 1 && f[[1, 1]] > 2]; Select[Prime /@ Range[2, 400], selQ] (* Jean-François Alcover, Nov 22 2013 *)

Prog

(PARI) is(n)=isprime(n) && n>4 && n%4==1 && isprimepower((n+1)/2) \\ Charles R Greathouse IV, Nov 22 2013

Crossrefs

Subsequence of A002144.

Sequence in context: A216575 A306626 A053028 * A248980 A188131 A172459

Adjacent sequences: A189408 A189409 A189410 * A189412 A189413 A189414

Keyword

nonn

Author

Luis H. Gallardo, Apr 21 2011

Extensions

Simpler name from Charles R Greathouse IV, Nov 22 2013

Status

approved