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 three values of i.
The asymptotic density of this sequence is 1 - (1 + s(1) + s(1)^2/2 - s(2)/2) * Product_{p prime} (1-1/p^3+1/p^4) = 0.000018992895371889141564..., where s(k) = Sum_{p prime} ((p-1)/(p^4-p+1))^k. - Amiram Eldar, Jul 22 2024
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
27000 is a term since 27000 = 2^3 * 3^3 * 5^3.
74088 is a term since 74088 = 2^3 * 5^3 * 7^3.
MATHEMATICA
f[n_]:=Count[Last/@FactorInteger[n], 3]>2; Select[Range[10!], f]
PROG
(PARI) is(n) = #select(x -> x == 3, factor(n)[, 2]) > 2; \\ Amiram Eldar, Jul 22 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Dec 07 2010
EXTENSIONS
Edited by Matthew Vandermast, Dec 09 2010
STATUS
approved