A120675 Number of prime factors of odd squarefree numbers A056911.

0, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 3, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 2, 2, 1, 3, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 3, 1, 2, 2, 1, 1, 2, 2, 1, 2, 3

Offset: 1

Author

Lekraj Beedassy, Jun 24 2006

Keywords

• nonn

Comments

For n>1, a(n)=1 corresponds to numbers n that are odd primes.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Programs

Maple

issquarefree := proc(n::integer) local nf, ifa ; nf := op(2,ifactors(n)) ; for ifa from 1 to nops(nf) do if op(2,op(ifa,nf)) >= 2 then RETURN(false) ; fi ; od : RETURN(true) ; end: A001221 := proc(n::integer) RETURN(nops(numtheory[factorset](n))) ; end: A056911 := proc(maxn) local n,a ; a := [1] ; for n from 3 to maxn by 2 do if issquarefree(n) then a := [op(a),n] ; fi ; od : RETURN(a) ; end: A120675 := proc(maxn) local a,n; a := A056911(maxn) ; for n from 1 to nops(a) do a := subsop(n=A001221(a[n]),a) ; od ; RETURN(a) ; end: nmax := 600 : a := A120675(nmax) : for n from 1 to nops(a) do printf("%d,",a[n]) ; od ; amer% # R. J. Mathar, Aug 17 2006

Mathematica

PrimeNu[Select[Range[1, 1000, 2], SquareFreeQ]] (* G. C. Greubel, May 11 2017 *)

Formula

a(n) = A001221(A056911(n)) = A001222(A056911(n)).

Extensions

Corrected and extended by R. J. Mathar, Aug 17 2006