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A325839 Exponentially-odd highly composite numbers: numbers with record values of the number of exponentially odd divisors (A325837). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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).

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..290

Amiram Eldar, Table of n, a(n), A325837(a(n)) for n = 1..290

MATHEMATICA

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

CROSSREFS

Cf. A033634, A046951, A046952, A268335, A325837.

Subsequence of A025487.

Sequence in context: A234272 A269077 A183915 * A081654 A307004 A264280

Adjacent sequences:  A325836 A325837 A325838 * A325840 A325841 A325842

KEYWORD

nonn

AUTHOR

Amiram Eldar, Sep 07 2019

STATUS

approved

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Last modified September 19 09:06 EDT 2020. Contains 337178 sequences. (Running on oeis4.)