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A325839
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Exponentially-odd coreful highly composite numbers: numbers with record values of the number of exponentially odd coreful divisors (A325837).
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1
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1, 8, 32, 128, 512, 864, 3456, 7776, 13824, 31104, 124416, 279936, 497664, 1119744, 1990656, 3888000, 10077696, 15552000, 34992000, 62208000, 139968000, 248832000, 388800000, 559872000, 1259712000, 1555200000, 2239488000, 3499200000, 6220800000, 8957952000
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OFFSET
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1,2
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COMMENTS
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The corresponding record numbers of exponentially-odd divisors are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 21, 24, 25, 30, 32, 36, 40, 42, 45, 48, 50, 54, 56, 60, 63, 64, ... (see the link for more terms).
The even version of this sequence is A046952 which is the sequence of numbers with record number of square divisors (only even exponents, A046951).
Numbers with record values of the number of exponentially odd divisors are the same as the numbers with record values of the number of semi-unitary divisors (A322484). - Amiram Eldar, Sep 08 2023
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LINKS
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MATHEMATICA
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fun[p_, e_] := Floor[(e+1)/2]; a[n_] := Times@@(fun@@@FactorInteger[n]); am = 0; s={}; Do[a1=a[n]; If[a1>am, am=a1; AppendTo[s, n]], {n, 1, 300000}]; s
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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