OFFSET
1,3
COMMENTS
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.
We define a co-mode in a multiset to be an element that appears at most as many times as each of the others. For example, the co-modes in {a,a,b,b,b,c,c} are {a,c}.
Extending the terminology of A124943, the "high co-mode" in a multiset is the greatest co-mode.
EXAMPLE
The prime indices of 2100 are {1,1,2,3,3,4}, with co-modes {2,4}, so a(2100) = 4.
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
comodes[ms_]:=Select[Union[ms], Count[ms, #]<=Min@@Length/@Split[ms]&];
Table[If[n==1, 0, Max[comodes[prix[n]]]], {n, 30}]
CROSSREFS
Ranking and counting partitions:
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 16 2023
STATUS
approved