This site is supported by donations to The OEIS Foundation.



Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A067259 Cubefree numbers which are not squarefree. 16


%S 4,9,12,18,20,25,28,36,44,45,49,50,52,60,63,68,75,76,84,90,92,98,99,

%T 100,116,117,121,124,126,132,140,147,148,150,153,156,164,169,171,172,

%U 175,180,188,196,198,204,207,212,220,225,228

%N Cubefree numbers which are not squarefree.

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

%C 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

%H Reinhard Zumkeller, <a href="/A067259/b067259.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Cubefree.html">Cubefree</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Squarefree.html">Squarefree</a>

%F A212793(a(n)) * (1 - A008966(a(n))) = 1. - _Reinhard Zumkeller_, May 27 2012

%t 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 *)

%o (Haskell)

%o a067259 n = a067259_list !! (n-1)

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

%o -- _Reinhard Zumkeller_, May 27 2012

%o (PARI) is(n)=n>3 && vecmax(factor(n)[,2])==2 \\ _Charles R Greathouse IV_, Oct 15 2015

%Y Cf. A004709, A005117.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Feb 20 2002

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 11 18:19 EST 2019. Contains 329925 sequences. (Running on oeis4.)