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A359465
a(n) = 1 if n is an odd squarefree number with an even number of prime factors, otherwise 0.
3
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0
OFFSET
1
FORMULA
a(n) = A000035(n) * A353629(n).
a(n) = A008966(n) * A353557(n) = A008966(n) * A353675(n).
a(n) = A065043(n) * A323239(n) = A323239(n) * A359464(n).
a(n) = [A343370(n) = 1], where [ ] is the Iverson bracket.
For all n >= 1, a(n) >= A353481(n).
Sum_{k=1..n} a(k) ~ c * n, where c = 2/Pi^2 (A185197). - Amiram Eldar, Jan 05 2023
MATHEMATICA
a[n_] := If[OddQ[n] && MoebiusMu[n] == 1, 1, 0]; Array[a, 100] (* Amiram Eldar, Jan 05 2023 *)
PROG
(PARI)
A065043(n) = (1 - (bigomega(n)%2));
A323239(n) = ((n%2) && issquarefree(n));
A359465(n) = (A323239(n)&&A065043(n));
CROSSREFS
Characteristic function of A056913.
After n=1 differs from A353481 for the next time at n=1155, where a(1155)=1, while A353481(1155)=0. Cf. also A046390.
Sequence in context: A249832 A014041 A373258 * A353675 A373137 A015868
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 02 2023
STATUS
approved