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A359912
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Numbers whose prime indices do not have integer median.
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37
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1, 6, 14, 15, 26, 33, 35, 36, 38, 51, 58, 60, 65, 69, 74, 77, 84, 86, 93, 95, 106, 119, 122, 123, 132, 141, 142, 143, 145, 150, 156, 158, 161, 177, 178, 185, 196, 201, 202, 204, 209, 210, 214, 215, 216, 217, 219, 221, 225, 226, 228, 249, 262, 265, 276, 278
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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.
The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
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LINKS
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EXAMPLE
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The terms together with their prime indices begin:
1: {}
6: {1,2}
14: {1,4}
15: {2,3}
26: {1,6}
33: {2,5}
35: {3,4}
36: {1,1,2,2}
38: {1,8}
51: {2,7}
58: {1,10}
60: {1,1,2,3}
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MATHEMATICA
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prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], !IntegerQ[Median[prix[#]]]&]
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CROSSREFS
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For prime factors instead of indices we have A072978, complement A359913.
These partitions are counted by A307683.
Cf. A026424, A051293, A067538, A175352, A175761, A289509, A359890, A359905, A360006, A359907, A360009.
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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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