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A360553
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Numbers > 1 whose unordered prime signature has integer median.
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11
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2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 46, 47, 49, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 81, 82, 83
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OFFSET
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1,1
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COMMENTS
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First differs from A067340 in having 60.
A number's unordered prime signature (row n of A118914) is the multiset of positive exponents in its prime factorization.
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 unordered prime signature of 60 is {1,1,2}, with median 1, so 60 is in the sequence.
The unordered prime signature of 1260 is {1,1,2,2}, with median 3/2, so 1260 is not in the sequence.
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MATHEMATICA
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Select[Range[2, 100], IntegerQ[Median[Last/@FactorInteger[#]]]&]
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CROSSREFS
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Positions of even terms in A360460.
The complement is A360554 (without 1).
These partitions are counted by A360687.
A360454 = numbers whose prime indices and signature have the same median.
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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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