cp's OEIS Frontend

A327500 Number of steps to reach a fixed point starting with n and repeatedly taking the quotient by the maximum divisor whose prime multiplicities are distinct (A327498, A327499).

%I A327500 #12 Apr 02 2022 17:48:01
%S A327500 0,1,1,1,1,2,1,1,1,2,1,1,1,2,2,1,1,1,1,1,2,2,1,1,1,2,1,1,1,3,1,1,2,2,
%T A327500 2,2,1,2,2,1,1,3,1,1,1,2,1,1,1,1,2,1,1,1,2,1,2,2,1,2,1,2,1,1,2,3,1,1,
%U A327500 2,3,1,1,1,2,1,1,2,3,1,1,1,2,1,2,2,2,2,1,1,2,2,1,2,2,2,1,1,1,1,2,1,3,1,1,3
%N A327500 Number of steps to reach a fixed point starting with n and repeatedly taking the quotient by the maximum divisor whose prime multiplicities are distinct (A327498, A327499).
%C A327500 A number's prime multiplicities are also called its (unsorted) prime signature. Numbers whose prime multiplicities are distinct are A130091.
%H A327500 Antti Karttunen, <a href="/A327500/b327500.txt">Table of n, a(n) for n = 1..65537</a>
%H A327500 Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vSX9dPMGJhxB8rOknCGvOs6PiyhupdWNpqLsnphdgU6MEVqFBnWugAXidDhwHeKqZe_YnUqYeGOXsOk/pub">Sequences counting and encoding certain classes of multisets</a>
%e A327500 We have 9282 -> 546 -> 42 -> 6 -> 2 -> 1, so a(9282) = 5.
%t A327500 Table[Length[FixedPointList[#/Max[Select[Divisors[#],UnsameQ@@Last/@FactorInteger[#]&]]&,n]]-2,{n,100}]
%o A327500 (PARI)
%o A327500 A351564(n) = issquarefree(factorback(apply(e->prime(e),(factor(n)[,2]))));
%o A327500 A327499(n) = fordiv(n,d,if(A351564(n/d), return(d)));
%o A327500 A327500(n) = { my(u=A327499(n)); if(u==n, 0, 1+A327500(u)); }; \\ _Antti Karttunen_, Apr 02 2022
%Y A327500 See link for additional cross-references.
%Y A327500 Position of first appearance of n is A002110(n).
%Y A327500 Cf. A000005, A056239, A098859, A112798, A124010, A130091, A255231, A327498, A327499, A351564.
%Y A327500 Cf. also A327503.
%K A327500 nonn
%O A327500 1,6
%A A327500 _Gus Wiseman_, Sep 16 2019
%E A327500 Data section extended up to 105 terms by _Antti Karttunen_, Apr 02 2022