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 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 (list; graph; refs; listen; history; text; internal format)
 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: 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

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Last modified January 18 06:34 EST 2019. Contains 319269 sequences. (Running on oeis4.)