A373136 a(n) = 1 if n is of the form 2^i * 3^j * k, i+j even, gcd(k,6)=1, otherwise 0.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions.

Formula

a(n) = [A007814(n)+A007949(n) == 0 (mod 2)], where [ ] is the Iverson bracket.

Sum_{k=1..n} a(k) ~ (7/12) * n. - Amiram Eldar, May 29 2024

Mathematica

a[n_] := If[EvenQ[Plus @@ IntegerExponent[n, {2, 3}]], 1, 0]; Array[a, 100] (* Amiram Eldar, May 29 2024 *)

Prog

(PARI) A373136(n) = !((valuation(n, 2)+valuation(n, 3))%2); \\ After function "is" in A036668

Crossrefs

Characteristic function of Hati numbers, A036668.

Cf. A007310, A007814, A007949.

Sequence in context: A090172 A284369 A194661 * A285427 A285621 A204435

Adjacent sequences: A373133 A373134 A373135 * A373137 A373138 A373139

Keyword

nonn,easy

Author

Antti Karttunen, May 28 2024

Status

approved