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A364158
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Numbers whose multiset of prime factors has low (i.e. least) co-mode 2.
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6
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1, 2, 4, 6, 8, 10, 14, 16, 18, 22, 26, 30, 32, 34, 36, 38, 42, 46, 50, 54, 58, 62, 64, 66, 70, 74, 78, 82, 86, 90, 94, 98, 100, 102, 106, 108, 110, 114, 118, 122, 126, 128, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182, 186, 190, 194
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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
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MATHEMATICA
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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&]
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CROSSREFS
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Partitions of this type are counted by A364159.
Ranking partitions:
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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