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

1,2

Links

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

Formula

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

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 *)

Crossrefs

Sequence in context: A355035 A105068 A363274 * A184172 A125973 A227196

Adjacent sequences: A120673 A120674 A120675 * A120677 A120678 A120679

Keyword

nonn

Author

Lekraj Beedassy, Jun 24 2006

Extensions

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

Status

approved