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

1,12

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)<n for m < A097250(n).

Links

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

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A035153 A069847 A238532 * A376846 A112313 A297115

Adjacent sequences: A097246 A097247 A097248 * A097250 A097251 A097252

Keyword

nonn

Author

Reinhard Zumkeller, Aug 03 2004

Extensions

Edited by Sam Alexander, Jan 05 2005

Status

approved