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A363131
Number of non-co-modes in the prime factorization of n.
7
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0
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
Positions of terms > 0 are A059404.
Positions of first appearances appear to converge to A228593.
For modes instead of non-co-modes we have A362611, triangle A362614.
For co-modes instead of non-co-modes we have A362613, triangle A362615.
For parts instead of multiplicities we have A362983.
For non-modes instead of non-co-modes we have A363127, triangle A363126.
The triangle for this rank statistic (number of non-co-modes) is A363130.
A027746 lists prime factors, A112798 indices, A124010 exponents.
A047966 counts uniform partitions, ranks A072774.
A363128 counts partitions with more than one non-mode, complement A363129.
Sequence in context: A353472 A359475 A294937 * A355447 A045701 A277156
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 18 2023
STATUS
approved