A056824 Numbers of the form p^(2k+1), p prime, k >= 1.

8, 27, 32, 125, 128, 243, 343, 512, 1331, 2048, 2187, 2197, 3125, 4913, 6859, 8192, 12167, 16807, 19683, 24389, 29791, 32768, 50653, 68921, 78125, 79507, 103823, 131072, 148877, 161051, 177147, 205379, 226981, 300763, 357911, 371293, 389017

Offset: 1

Author

Labos Elemer, Aug 29 2000

Keywords

• nonn

Links

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

Crossrefs

Cf. A025475, A000961, A369632.

Programs

PARI

is(n)=my(e=isprimepower(n)); e>1 && e%2 \\ Charles R Greathouse IV, Jan 15 2015

PARI

list(lim)=my(v=List(apply(k->k^3, primes([2,sqrtnint(lim\1,3)]))),t); forstep(e=5,log(lim+.5)\log(2),2, forprime(p=2,,t=p^e; if(t>lim, break); listput(v,t))); Set(v) \\ Charles R Greathouse IV, Jan 15 2015

Formula

a(n) ~ n^3 log^3 n. - Charles R Greathouse IV, Jan 15 2015

Sum_{n>=1} 1/a(n) = Sum_{p prime} 1/(p*(p^2-1)) = 0.2214633713... (A369632). - Amiram Eldar, Dec 23 2020

Extensions

Name edited by Altug Alkan, following a suggestion by Felix Fröhlich, May 17 2018