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

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

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

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

Mathematica

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

Prog

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

Crossrefs

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

Cf. also A066503.

Sequence in context: A389072 A299163 A388991 * A369931 A160086 A115869

Adjacent sequences: A326125 A326126 A326127 * A326129 A326130 A326131

Keyword

nonn

Author

Antti Karttunen, Jun 09 2019

Status

approved