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A363127
Number of non-modes in the multiset of prime factors of n.
8
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, 2, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0
OFFSET
1,60
COMMENTS
A non-mode in a multiset is an element that appears fewer times than at least one of the others. For example, the non-modes in {a,a,b,b,b,c,d,d,d} are {a,c}.
EXAMPLE
The prime factorization of 13860 is 2*2*3*3*5*7*11, with non-modes {5,7,11}, so a(13860) = 3.
MATHEMATICA
prifacs[n_]:=If[n==1, {}, Flatten[ConstantArray@@@FactorInteger[n]]];
nmsi[ms_]:=Select[Union[ms], Count[ms, #]<Max@@Length/@Split[ms]&];
Table[Length[nmsi[prifacs[n]]], {n, 100}]
CROSSREFS
Positions of first appearances converge to A088860.
For modes instead of non-modes we have A362611, triangle A362614.
For co-modes instead of non-modes we have A362613, triangle A362615.
The triangle for this rank statistic (number of non-modes) is A363126.
For non-co-modes instead of non-modes we have A363131, triangle A363130.
A027746 lists prime factors, A112798 indices, A124010 exponents.
A047966 counts uniform partitions, ranks A072774.
A363124 counts partitions with more than one non-mode, complement A363125.
Sequence in context: A065335 A230264 A374208 * A088534 A178602 A363711
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 16 2023
STATUS
approved