OFFSET
1,1
COMMENTS
In other words, if the canonical prime factorization of a term into prime powers is Product p(i)^e(i), then e(i) = 3 for at least two values of i.
Does not include all numbers with at least two unitary prime power divisors that are cubes (see example section).
The asymptotic density of this sequence is 1 - (1 + Sum_{p prime} ((p-1)/(p^4-p+1))) * Product_{p prime} (1-1/p^3+1/p^4) = 0.0024593812036570543518... . - Amiram Eldar, Jul 22 2024
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
EXAMPLE
216 = 2^3*3^3, 1000 = 2^3*5^3, 1080 = 2^3*3^3*5, ...
On the other hand, 1728 = 2^6*3^3, 8000 = 2^6*5^3 and 21952 = 2^6*7^3 are not in the sequence.
MATHEMATICA
f[n_]:=Count[Last/@FactorInteger[n], 3]>1; Select[Range[8!], f]
PROG
(PARI) is(n)=#select(e->e==3, factor(n)[, 2])>1 \\ Charles R Greathouse IV, Oct 19 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, Dec 07 2010
EXTENSIONS
Edited by Matthew Vandermast, Dec 07 2010
STATUS
approved