A340373 a(n) = 1 if n is of the form of 2^i * p^j, with p an odd prime, and i>=0, j>=1, otherwise 0.

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

Offset

1

Comments

a(n) = 1 if the odd part of n has exactly one distinct prime divisor, and 0 otherwise.

Links

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

Index entries for characteristic functions

Formula

a(n) = A069513(A000265(n)).

a(n) = [A005087(n) == 1], where [ ] is the Iverson bracket, and A005087(n) = A001221(A000265(n)).

a(n) = A340363(n) - A209229(n).

a(n) = Sum_{d|n} mu(2*d)*bigomega(d). - Ridouane Oudra, Oct 29 2024

Mathematica

A340373[n_] := Boole[PrimePowerQ[n/2^IntegerExponent[n, 2]]]; Array[A340373, 100] (* Paolo Xausa, Oct 31 2024 *)

Prog

(PARI) A340373(n) = (1==omega(n>>valuation(n, 2)));

Crossrefs

Cf. A000265, A001221, A005087, A069513, A209229, A340363.

Characteristic function of A336101.

Sequence in context: A295309 A353670 A252744 * A043545 A094754 A321694

Adjacent sequences: A340370 A340371 A340372 * A340374 A340375 A340376

Keyword

nonn

Author

Antti Karttunen, Jan 06 2021

Status

approved