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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.
4
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
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
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: A044939 A373973 A371084 * A347244 A366289 A037824
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 02 2022
STATUS
approved