login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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