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A353500
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Numbers that are the smallest number with product of prime exponents k for some k. Sorted positions of first appearances in A005361, unsorted version A085629.
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9
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1, 4, 8, 16, 32, 64, 128, 144, 216, 288, 432, 864, 1152, 1296, 1728, 2048, 2592, 3456, 5184, 7776, 8192, 10368, 13824, 15552, 18432, 20736, 31104, 41472, 55296, 62208, 73728, 86400, 108000, 129600, 131072, 165888, 194400, 216000, 221184, 259200, 279936, 324000
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OFFSET
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1,2
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COMMENTS
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All terms are highly powerful (A005934), but that sequence looks only at first appearances that reach a record, and is missing 1152, 2048, 8192, etc.
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LINKS
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EXAMPLE
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The prime exponents of 86400 are (7,3,2), and this is the first case of product 42, so 86400 is in the sequence.
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MATHEMATICA
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nn=1000;
d=Table[Times@@Last/@FactorInteger[n], {n, nn}];
Select[Range[nn], !MemberQ[Take[d, #-1], d[[#]]]&]
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CROSSREFS
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These are the positions of first appearances in A005361, counted by A266477.
This is the sorted version of A085629.
The version for shadows instead of exponents is A353397, firsts in A353394.
A130091 lists numbers with distinct prime exponents, counted by A098859.
Cf. A070175, A097318, A116608, A182850, A304678, A325131, A325238, A353399, A353503, A353506, A353507.
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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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