A379970 a(n) = 1 if n is twice its squarefree kernel (A007949), otherwise 0.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions.

Formula

a(n) = [n = 2*A007947(n)], where [ ] is the Iverson bracket.

a(n) = [A280292(n) = 2].

Sum_{k=1..n} a(k) ~ n/Pi^2. - Amiram Eldar, Jan 22 2025

Mathematica

a[n_] := Boole[IntegerExponent[n, 2] == 2 && SquareFreeQ[n/4]]; Array[a, 100] (* Amiram Eldar, Jan 22 2025 *)

Prog

(PARI) A379970(n) = (n == 2*factorback(factorint(n)[, 1]));

Crossrefs

Characteristic function of A081770, numbers twice their squarefree kernel (A007947).

Cf. A008966, A092742, A280292, A379966.

Sequence in context: A346459 A193243 A281302 * A369426 A340599 A160753

Adjacent sequences: A379967 A379968 A379969 * A379971 A379972 A379973

Keyword

nonn

Author

Antti Karttunen, Jan 22 2025

Status

approved