A101040 If n has one or two prime-factors then 1 else 0.

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

Offset

1,1

Comments

a(A033942(n))=0; for n>1: a(A037143(n))=1;

a(A000040(n))=1; a(A001358(n))=1;

A101041(n) = Sum(a(k): 1<=k<=n) + 1.

Primes counted with multiplicity. - Harvey P. Dale, Feb 16 2024

Links

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

Index entries for characteristic functions

Index entries for sequences computed from exponents in factorization of n

Formula

a(n) = A010051(n)+A064911(n) = 0^floor(A001222(n)/3)-0^(n-1).

a(1) = 0; for n > 1, a(n) = A063524(A032742(A032742(n))). - Antti Karttunen, Nov 23 2017

Mathematica

a[n_] := If[n == 1, 0, Boole[PrimeOmega[n] <= 2]];
Array[a, 105] (* Jean-François Alcover, Dec 02 2021 *)

Prog

(Scheme) (define (A101040 n) (if (= 1 n) 0 (A063524 (A032742 (A032742 n))))) ;; Antti Karttunen, Nov 23 2017
(PARI) vector(105, k, bigomega(k)<=2&&k>1) \\ Hugo Pfoertner, Dec 02 2021

Crossrefs

Characteristic function of A037143 (without its initial term 1).

Sequence in context: A135947 A360123 A211487 * A341591 A306453 A175629

Adjacent sequences: A101037 A101038 A101039 * A101041 A101042 A101043

Keyword

nonn

Author

Reinhard Zumkeller, Nov 28 2004

Status

approved