OFFSET
1,2
COMMENTS
This sequence is closed under multiplication.
The least term that is not a power of a prime (A000961) is a(25) = 7^2*11^2 = 5929.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Rough Number.
FORMULA
Sum_{n>=1} 1/a(n) = 80*zeta(2)*zeta(3)/(147*zeta(6)) = (80/147) * A082695 = 1.05773955745... .
In general, the sum of reciprocals of the p-rough powerful numbers is (zeta(2)*zeta(3)/zeta(6)) * Product_{prime q < p} ((q-1)*q/(q^2-q+1)).
MATHEMATICA
powQ[n_] := n == 1 || AllTrue[FactorInteger[n][[;; , 2]], # > 1 &]; Select[Range[20000], CoprimeQ[#, 30] && powQ[#] &]
PROG
(PARI) is(k) = gcd(k, 30) == 1 && ispowerful(k);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Jul 02 2024
STATUS
approved