cp's OEIS Frontend

A327538 Number of steps to reach a fixed point starting with n and repeatedly taking the quotient by the maximum divisor that is 1, prime, or whose prime indices are relatively prime (A327535, A327537).

%I A327538 #6 Sep 18 2019 04:58:21
%S A327538 0,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,2,1,3,1,1,1,1,1,1,1,
%T A327538 1,1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1,1,1,3,1,2,1,1,1,
%U A327538 1,1,1,1,1,1,1,1,1,1,1,1,4,1,1,1,1,1,2
%N A327538 Number of steps to reach a fixed point starting with n and repeatedly taking the quotient by the maximum divisor that is 1, prime, or whose prime indices are relatively prime (A327535, A327537).
%C A327538 The first index m such that a(m) > 1 but m is not in A322336 is m = 2335.
%C A327538 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. Numbers that are 1, prime, or whose prime indices are relatively prime are A327534. The number of divisors of n satisfying the same conditions is A327536(n).
%H A327538 Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vSX9dPMGJhxB8rOknCGvOs6PiyhupdWNpqLsnphdgU6MEVqFBnWugAXidDhwHeKqZe_YnUqYeGOXsOk/pub">Sequences counting and encoding certain classes of multisets</a>
%F A327538 a(1) = 0; if n is prime or has relatively prime prime indices, then a(n) = 1; otherwise a(n) = Omega(n) = A001222(n).
%e A327538 We have 441 -> 63 -> 9 -> 3 -> 1, so a(441) = 4.
%t A327538 Table[Length[FixedPointList[#/Max[Select[Divisors[#],#==1||PrimeQ[#]||GCD@@PrimePi/@First/@FactorInteger[#]==1&]]&,n]]-2,{n,100}]
%Y A327538 See link for additional cross-references.
%Y A327538 Cf. A000005, A001222, A006530, A056239, A112798, A289509, A327407.
%K A327538 nonn
%O A327538 1,9
%A A327538 _Gus Wiseman_, Sep 17 2019