A327515 Number of steps to reach a fixed point starting with n and repeatedly taking the quotient by the maximum divisor that is 1, 2, or a nonprime number whose prime indices are pairwise coprime (A327512, A327514).
0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1
Offset: 1
Keywords
Examples
We have 50625 -> 3375 -> 225 -> 15 -> 1, so a(50625) = 4.
Links
Crossrefs
Programs
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Mathematica
primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]; Table[Length[FixedPointList[#/Max[Select[Divisors[#],#==1||CoprimeQ@@primeMS[#]&]]&,n]]-2,{n,100}] -
PARI
isA302696(n) = if(isprimepower(n), !(n%2), if(!issquarefree(n>>valuation(n, 2)), 0, my(pis=apply(primepi, factor(n)[, 1])); (lcm(pis)==factorback(pis)))); A327512(n) = vecmax(select(isA302696, divisors(n))); A327515(n) = for(k=0,oo,my(nextn=n/A327512(n)); if(nextn==n,return(k)); n = nextn); \\ Antti Karttunen, Jan 28 2025
Formula
a(15^n) = n.
Extensions
Data section extended to a(105) and secondary offset added by Antti Karttunen, Jan 28 2025
Comments