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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).
8
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, 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, 2, 3, 1, 2, 1, 2, 2, 2, 2, 3, 1, 2, 4, 2, 1, 2, 2, 2, 2
OFFSET
1,4
LINKS
EXAMPLE
The following are examples showing the reduction of a multiset starting with the multiset of prime multiplicities of n.
a(60) = 2: {1,1,2} -> {1,2} -> {1,1}.
a(360) = 3: {1,2,3} -> {1,1,1}.
a(1260) = 4: {1,1,2,2} -> {2,2}.
a(21492921450) = 6: {1,1,2,2,3,3} -> {2,2,2}.
MAPLE
a:= proc(n) map(i-> i[2], ifactors(n)[2]);
while nops({%[]})>1 do [coeffs(add(x^i, i=%))] od;
add(i, i=%)
end:
seq(a(n), n=1..100); # Alois P. Heinz, May 17 2018
MATHEMATICA
Table[If[n==1, 0, NestWhile[Sort[Length/@Split[#]]&, Sort[Last/@FactorInteger[n]], !SameQ@@#&]//Total], {n, 360}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 16 2018
STATUS
approved