A325839 Exponentially-odd coreful highly composite numbers: numbers with record values of the number of exponentially odd coreful divisors (A325837).

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

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).

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

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, A322484, A325837.

Subsequence of A025487.

Sequence in context: A358253 A358252 A374159 * A379593 A081654 A307004

Adjacent sequences: A325836 A325837 A325838 * A325840 A325841 A325842

Keyword

nonn

Author

Amiram Eldar, Sep 07 2019

Extensions

Name corrected by Amiram Eldar, Sep 08 2023

Status

approved