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

1,7

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

Formula

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

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 *)

Crossrefs

Sequence in context: A191774 A262885 A097305 * A072699 A143589 A003651

Adjacent sequences: A120672 A120673 A120674 * A120676 A120677 A120678

Keyword

nonn

Author

Lekraj Beedassy, Jun 24 2006

Extensions

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

Status

approved