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

Author

Amiram Eldar, Sep 07 2019

Keywords

• nonn

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

Crossrefs

Cf. A033634, A046951, A046952, A268335, A322484, A325837.

Subsequence of A025487.

Programs

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

Extensions

Name corrected by Amiram Eldar, Sep 08 2023