A340363 a(n) = 1 if n is of the form of 2^i * p^j, with p an odd prime and i, j >= 0, otherwise 0.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 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, 1, 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 no more than 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) = A010055(A000265(n)).

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

a(n) = A209229(n) + A340373(n).

For all n, a(n) <= A340372(n).

Mathematica

A340363[n_] := Boole[PrimeNu[n/2^IntegerExponent[n, 2]] < 2];
Array[A340363, 100] (* Paolo Xausa, Oct 31 2024 *)

Prog

(PARI)
A000265(n) = (n>>valuation(n, 2));
A340363(n) = (omega(A000265(n))<=1);

Crossrefs

Cf. A000265, A001221, A005087, A010055, A209229, A340372, A340373.

Characteristic function of {1} U A070776.

Sequence in context: A133011 A296079 A354806 * A340372 A167850 A167851

Adjacent sequences: A340360 A340361 A340362 * A340364 A340365 A340366

Keyword

nonn

Author

Antti Karttunen, Jan 06 2021

Status

approved