A369965 a(n) = 1 if n is of the form 4m+2 and it has an even number of prime factors with multiplicity, otherwise 0.

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

Offset

0

Links

Antti Karttunen, Table of n, a(n) for n = 0..100000

Index entries for characteristic functions

Formula

All these formulas should be computed with a shortcut multiplication, which ignores the right hand side expression if the left hand side yields zero:

a(n) = A121262(2+n) * A065043(n).

a(n) = A165560(n) * A065043(n).

a(n) = A059841(n) * A353558(n/2).

Mathematica

A369965[n_] := Boole[Mod[n, 4] == 2 && EvenQ[PrimeOmega[n]]];
Array[A369965, 100, 0] (* Paolo Xausa, Jan 21 2026 *)

Prog

(PARI) A369965(n) = (2==(n%4) && !(bigomega(n)%2));

Crossrefs

Characteristic function of A369966.

Cf. A059841, A065043, A121262, A165560, A353558.

Cf. A369660 [= a(A003415(n))].

Sequence in context: A070108 A341995 A369655 * A011675 A096094 A265757

Adjacent sequences: A369962 A369963 A369964 * A369966 A369967 A369968

Keyword

nonn

Author

Antti Karttunen, Feb 08 2024

Status

approved