A326128 a(n) = n - A007913(n), where A007913 gives the squarefree part of n.

0, 0, 0, 3, 0, 0, 0, 6, 8, 0, 0, 9, 0, 0, 0, 15, 0, 16, 0, 15, 0, 0, 0, 18, 24, 0, 24, 21, 0, 0, 0, 30, 0, 0, 0, 35, 0, 0, 0, 30, 0, 0, 0, 33, 40, 0, 0, 45, 48, 48, 0, 39, 0, 48, 0, 42, 0, 0, 0, 45, 0, 0, 56, 63, 0, 0, 0, 51, 0, 0, 0, 70, 0, 0, 72, 57, 0, 0, 0, 75, 80, 0, 0, 63, 0, 0, 0, 66, 0, 80, 0, 69, 0, 0, 0, 90, 0, 96, 88, 99, 0, 0, 0, 78, 0

Offset: 1

Author

Antti Karttunen, Jun 09 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537.

Crossrefs

Cf. A007913, A033879, A326126, A326127, A326129, A336642.

Cf. also A066503.

Programs

Mathematica

f[p_, e_] := p^Mod[e, 2]; a[n_] := n - Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Mar 21 2024 *)

PARI

A326128(n) = (n-core(n));

Formula

a(n) = n - A007913(n).

a(n) = A326127(n) + A033879(n).

a(n) >= A066503(n).

a(n) = A007913(n) * A336642(n). - Antti Karttunen, Jul 28 2020

Sum_{k=1..n} a(k) ~ c * n^2, where c = 1/2 - Pi^2/30 = 0.171013... . - Amiram Eldar, Mar 21 2024