OFFSET
1,1
COMMENTS
The sequence of numbers whose number of powerful divisors (including 1, A005361) is even is A072587, which is the sequence of numbers that are not exponentially odd (A268335).
The primitive terms of this sequence are the powerful terms (A376217). If m is a powerful term then k*m is a term of this sequence for all squarefree numbers k that are coprime to m.
Numbers that have at least one odd prime factor in their prime factorization that has an even exponent.
Also, numbers k such that A335341(k) is even.
The asymptotic density of this sequence is 1 - (6/5) * A065463 = 0.15466935880100128871... .
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
MATHEMATICA
q[n_] := Module[{f = Select[FactorInteger[n], First[#] == 2 || Last[#] > 1 &], i = 2 - Mod[n, 2]}, Length[f] > 0 && AnyTrue[f[[i;; -1, 2]], EvenQ]]; Select[Range[400], q]
PROG
(PARI) is(k) = {my(f = factor(k), i = 1 + !(k % 2)); #select(x -> !(x%2), f[i..#f~, 2]) > 0; }
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 15 2024
STATUS
approved