A353626 a(n) = 1 if n is a multiple of the square of an odd prime (equally: if the odd part of n is not squarefree), otherwise 0.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions.

Formula

a(n) = A107078(A000265(n)).

a(n) = a(2n) = a(A000265(n)).

a(n) = 1 - A353627(n) = 1 - abs(A209635(n)).

For all n >= 1, a(n) >= A353625(n) and (1-a(n)) * A166486(n) = A008966(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 - 8/Pi^2 = 0.189430... . - Amiram Eldar, Jul 24 2022

Mathematica

a[n_] := If[AnyTrue[FactorInteger[n/2^IntegerExponent[n, 2]][[;; , 2]], # > 1 &], 1, 0]; Array[a, 100] (* Amiram Eldar, Jul 24 2022 *)

Prog

(PARI) A353626(n) = !issquarefree(n>>valuation(n, 2));

Crossrefs

Cf. A000265, A008966, A107078, A166486, A209635, A353625.

Characteristic function of A038838, binary complement of A353627.

After n=1 differs from A347246 for the next time at n=153, where a(153) = 1, while A347246(153) = 0.

Sequence in context: A353477 A044939 A371084 * A347244 A366289 A037824

Adjacent sequences: A353623 A353624 A353625 * A353627 A353628 A353629

Keyword

nonn

Author

Antti Karttunen, May 02 2022

Status

approved