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A056824
Numbers of the form p^(2k+1), p prime, k >= 1.
6
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
1,1
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
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
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Aug 29 2000
EXTENSIONS
Name edited by Altug Alkan, following a suggestion by Felix Fröhlich, May 17 2018
STATUS
approved