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A067259 Cubefree numbers which are not squarefree. 13
4, 9, 12, 18, 20, 25, 28, 36, 44, 45, 49, 50, 52, 60, 63, 68, 75, 76, 84, 90, 92, 98, 99, 100, 116, 117, 121, 124, 126, 132, 140, 147, 148, 150, 153, 156, 164, 169, 171, 172, 175, 180, 188, 196, 198, 204, 207, 212, 220, 225, 228 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n)=m iff A051903(m)=2.

Let us introduce a function D(n)=sigma_0(n)/(2^(alpha(1)+...+alpha(r)), sigma_0(n) number of divisors of n (A000005), prime factorization of n=p(1)^alpha(1) * ... * p(r)^alpha(r), alpha(1)+...+alpha(r) is sequence (A086436). This function splits the set of positive integers into subsets, according to the value of D(n). Squarefree numbers (005117) has D(n)=1, other numbers are "deviated" from the squarefree ideal and have 0 < D(n) < 1. So for D(n)=1/2 we have A048109, D(n)=3/4 we have A067295. - Ctibor O. Zizka, Sep 21 2008

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Cubefree

Eric Weisstein's World of Mathematics, Squarefree

FORMULA

A212793(a(n)) * (1 - A008966(a(n))) = 1. - Reinhard Zumkeller, May 27 2012

MATHEMATICA

f[n_]:=Union[Last/@FactorInteger[n]][[ -1]]; lst={}; Do[If[f[n]==2, AppendTo[lst, n]], {n, 2, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 12 2010 *)

PROG

(Haskell)

a067259 n = a067259_list !! (n-1)

a067259_list = filter ((== 2) . a051903) [1..]

-- Reinhard Zumkeller, May 27 2012

(PARI) is(n)=n>3 && vecmax(factor(n)[, 2])==2 \\ Charles R Greathouse IV, Oct 15 2015

CROSSREFS

Cf. A004709, A005117.

Sequence in context: A081619 A304365 A038109 * A060687 A286228 A312863

Adjacent sequences:  A067256 A067257 A067258 * A067260 A067261 A067262

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Feb 20 2002

STATUS

approved

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Last modified October 19 17:55 EDT 2018. Contains 316376 sequences. (Running on oeis4.)