OFFSET
1
COMMENTS
We define a non-co-mode in a multiset to be an element that appears more times than at least one of the others. For example, the non-co-modes in {a,a,b,b,b,c,d,d,d} are {a,b,d}.
EXAMPLE
The prime factorization of 360 is 2*2*2*3*3*5, with non-co-modes {2,3}, so a(360) = 2.
MATHEMATICA
prifacs[n_]:=If[n==1, {}, Flatten[ConstantArray@@@FactorInteger[n]]];
ncomsi[ms_]:=Select[Union[ms], Count[ms, #]>Min@@Length/@Split[ms]&];
Table[Length[ncomsi[prifacs[n]]], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 18 2023
STATUS
approved