

A189411


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


1



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
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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(n1));
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] (* JeanFrançois 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: A191108 A216575 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



