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A120676
Number of prime factors of even squarefree numbers A039956.
1
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
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
KEYWORD
nonn
AUTHOR
Lekraj Beedassy, Jun 24 2006
EXTENSIONS
Corrected and extended by R. J. Mathar, Aug 17 2006
STATUS
approved