A353626 - OEIS

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

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OFFSET

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