A097249 a(n) is the number of times we must iterate A097246, starting at n, before the result is squarefree.

0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 2, 1, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 3, 0, 0, 1, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 3, 2, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 1, 1, 0, 0, 0, 1, 0

Offset: 1

Author

Reinhard Zumkeller, Aug 03 2004

Keywords

• nonn

Comments

a(n) = Min{k: r(n,k)=r(n,k+1)}, where r(n,k)=A097246(r(n,k-1)), r(n,0)=n;

a(A005117(n))=0; a(A097250(n))=n and a(m)A097250(n).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A005117, A097246, A097248, A097250, A277899.

Programs

Mathematica

f[n_] := Product[{p, e} = pe; NextPrime[p]^Quotient[e, 2] p^Mod[e, 2], {pe, FactorInteger[n]}];
a[n_] := (NestWhileList[f, n, !SquareFreeQ[#]&] // Length) - 1;
Array[a, 105] (* Jean-François Alcover, Nov 18 2021 *)

PARI

A097246(n) = { my(f=factor(n)); prod(i=1, #f~, (nextprime(f[i,1]+1)^(f[i,2]\2))*((f[i,1])^(f[i,2]%2))); };
A097249(n) = if(issquarefree(n),0,1+A097249(A097246(n))); \\ Antti Karttunen, Jul 29 2018

Formula

If A008966(n) = 1 [when n is in A005117], a(n) = 0, otherwise a(n) = 1 + a(A097246(n)). - Antti Karttunen, Jul 29 2018

Extensions

Edited by Sam Alexander, Jan 05 2005