A120676 Number of prime factors of even squarefree numbers A039956.

1, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 3, 3, 2, 3, 2, 2, 2, 3, 2, 3, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 3, 3, 2, 3, 3, 3, 2, 2, 2, 4, 2, 2, 3, 2, 3, 3, 3, 2, 3, 2, 3, 2, 2, 3, 3, 3, 2, 2, 3, 2, 3, 3, 2, 4, 2, 2, 3, 2, 2, 3, 3, 3, 2, 2, 4, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 2, 2, 4, 2, 3, 3, 2, 2, 3, 3, 2, 3, 4

Offset: 1

Author

Lekraj Beedassy, Jun 24 2006

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

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: A039956 := proc(maxn) local n,a ; a := [2] ; for n from 4 to maxn by 2 do if issquarefree(n) then a := [op(a),n] ; fi ; od : RETURN(a) ; end: A120676 := proc(maxn) local a,n; a := A039956(maxn) ; for n from 1 to nops(a) do a := subsop(n=A001221(a[n]),a) ; od ; RETURN(a) ; end: nmax := 600 : a := A120676(nmax) : for n from 1 to nops(a) do printf("%d,",a[n]) ; od ; # R. J. Mathar, Aug 17 2006

Mathematica

A264387[n_] := (# - 2)/4 & /@ Select[2 Range@n, SquareFreeQ]; A039956[n_] := 2*(1 + 2*A264387[n]); PrimeNu[A039956[50]] (* G. C. Greubel, May 16 2017 *)
PrimeOmega/@Select[2*Range[300],SquareFreeQ] (* Harvey P. Dale, Jul 28 2019 *)

Formula

a(n) = A001221(A039956(n)) = A001222(A039956(n)) = A120675(n)+1.

Extensions

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