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Search: id:A120675
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| A120675 |
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Number of prime factors of odd square-free numbers A056911. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,7
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COMMENT
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For n>1,a(n)=1 corresponds to n which are odd primes.
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FORMULA
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a(n)=A001221(A056911(n))=A001222(A056911(n)).
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MAPLE
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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 (mathar(AT)strw.leidenuniv.nl), Aug 17 2006
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CROSSREFS
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Sequence in context: A042974 A020906 A097305 this_sequence A072699 A003651 A073203
Adjacent sequences: A120672 A120673 A120674 this_sequence A120676 A120677 A120678
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KEYWORD
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nonn
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 24 2006
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EXTENSIONS
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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 17 2006
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