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%I #12 Jul 28 2019 18:31:12
%S 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,
%T 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,
%U 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
%N Number of prime factors of even squarefree numbers A039956.
%H G. C. Greubel, <a href="/A120676/b120676.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A001221(A039956(n)) = A001222(A039956(n)) = A120675(n)+1.
%p 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
%t 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 *)
%t PrimeOmega/@Select[2*Range[300],SquareFreeQ] (* _Harvey P. Dale_, Jul 28 2019 *)
%K nonn
%O 1,2
%A _Lekraj Beedassy_, Jun 24 2006
%E Corrected and extended by _R. J. Mathar_, Aug 17 2006