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

Author

Reinhard Zumkeller, Nov 28 2004

Keywords

• nonn

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

Crossrefs

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

Programs

Mathematica

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

PARI

vector(105,k,bigomega(k)<=2&&k>1) \\ Hugo Pfoertner, Dec 02 2021

Scheme

(define (A101040 n) (if (= 1 n) 0 (A063524 (A032742 (A032742 n))))) ;; Antti Karttunen, Nov 23 2017

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