OFFSET
1,2
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}.
Except for 1, this is the lists of all even numbers whose prime factorization contains at most as many 2's as non-2 parts.
Extending the terminology of A124943, the "low co-mode" of a multiset is the least co-mode.
EXAMPLE
The terms together with their prime factorizations begin:
1 =
2 = 2
4 = 2*2
6 = 2*3
8 = 2*2*2
10 = 2*5
14 = 2*7
16 = 2*2*2*2
18 = 2*3*3
22 = 2*11
26 = 2*13
30 = 2*3*5
32 = 2*2*2*2*2
34 = 2*17
36 = 2*2*3*3
MATHEMATICA
prifacs[n_]:=If[n==1, {}, Flatten[ConstantArray@@@FactorInteger[n]]];
comodes[ms_]:=Select[Union[ms], Count[ms, #]<=Min@@Length/@Split[ms]&];
Select[Range[100], #==1||Min[comodes[prifacs[#]]]==2&]
CROSSREFS
Partitions of this type are counted by A364159.
Ranking partitions:
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 14 2023
STATUS
approved