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A359158
a(n) = 1 if the odd part of n is squarefree and the number of prime factors of n (with multiplicity) is odd, otherwise 0.
5
0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0
OFFSET
1
COMMENTS
a(n) = 1 if A000265(n) is squarefree and A001222(n) is odd, otherwise 0.
FORMULA
a(n) = A066829(n) * A353627(n).
a(n) = A353627(n) - A359156(n).
a(n) = [A355689(n) < 0], where [ ] is the Iverson bracket.
a(n) >= A010051(n).
Sum_{k=1..n} a(k) ~ (4/Pi^2)*n. - Amiram Eldar, Jan 18 2023
MATHEMATICA
a[n_] := If[OddQ[PrimeOmega[n]] && SquareFreeQ[n/2^IntegerExponent[n, 2]], 1, 0]; Array[a, 100] (* Amiram Eldar, Jan 18 2023 *)
PROG
(PARI) A359158(n) = ((bigomega(n)%2)&&issquarefree(n>>valuation(n, 2)));
CROSSREFS
Characteristic function of A359159.
Sequence in context: A353817 A374474 A284653 * A099104 A358769 A066829
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 20 2022
STATUS
approved