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A097249 a(n) is the number of times we must iterate A097246, starting at n, before the result is squarefree. 7
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 (list; graph; refs; listen; history; text; internal format)
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 * A112313 A297115 A337346

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

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Last modified December 4 18:08 EST 2021. Contains 349526 sequences. (Running on oeis4.)