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A304687 Start with the multiset of prime multiplicities of n. Given a multiset, take the multiset of its multiplicities. Repeat until a constant multiset {k,k,...,k} is reached, and set a(n) to the sum of this multiset (k times the length).

%I A304687 #14 Jun 05 2018 14:18:16
%S A304687 0,1,1,2,1,2,1,3,2,2,1,2,1,2,2,4,1,2,1,2,2,2,1,2,2,2,3,2,1,3,1,5,2,2,
%T A304687 2,4,1,2,2,2,1,3,1,2,2,2,1,2,2,2,2,2,1,2,2,2,2,2,1,2,1,2,2,6,2,3,1,2,
%U A304687 2,3,1,2,1,2,2,2,2,3,1,2,4,2,1,2,2,2,2
%N A304687 Start with the multiset of prime multiplicities of n. Given a multiset, take the multiset of its multiplicities. Repeat until a constant multiset {k,k,...,k} is reached, and set a(n) to the sum of this multiset (k times the length).
%H A304687 Alois P. Heinz, <a href="/A304687/b304687.txt">Table of n, a(n) for n = 1..20000</a>
%e A304687 The following are examples showing the reduction of a multiset starting with the multiset of prime multiplicities of n.
%e A304687          a(60) = 2: {1,1,2} -> {1,2} -> {1,1}.
%e A304687         a(360) = 3: {1,2,3} -> {1,1,1}.
%e A304687        a(1260) = 4: {1,1,2,2} -> {2,2}.
%e A304687 a(21492921450) = 6: {1,1,2,2,3,3} -> {2,2,2}.
%p A304687 a:= proc(n) map(i-> i[2], ifactors(n)[2]);
%p A304687       while nops({%[]})>1 do [coeffs(add(x^i, i=%))] od;
%p A304687       add(i, i=%)
%p A304687     end:
%p A304687 seq(a(n), n=1..100);  # _Alois P. Heinz_, May 17 2018
%t A304687 Table[If[n==1,0,NestWhile[Sort[Length/@Split[#]]&,Sort[Last/@FactorInteger[n]],!SameQ@@#&]//Total],{n,360}]
%Y A304687 Cf. A001221, A001222, A071625, A112798, A181819, A182850, A182857, A304465, A304634, A304636.
%K A304687 nonn
%O A304687 1,4
%A A304687 _Gus Wiseman_, May 16 2018