A307845 Exponential unitary highly composite numbers: where the number of exponential unitary divisors (A278908) increases to a record.

1, 4, 36, 576, 14400, 705600, 57153600, 6915585600, 1168733966400, 337764116289600, 121932845980545600, 64502475523708622400, 40314047202317889000000, 33904113697149344649000000, 32581853262960520207689000000, 44604557116992952164326241000000, 74980260513665152588232411121000000

Offset: 1

Author

Amiram Eldar, May 01 2019

Keywords

• nonn

Comments

Subsequence of A025487.

All the terms have prime factors with multiplicities which are primorials > 1 (the primorials, A002110, are the unitary highly composite numbers), similarly to exponential highly composite numbers (A318278) whose prime factors have multiplicities which are highly composite numbers (A002182). Thus all the terms are squares. Their square roots are 1, 2, 6, 24, 120, 840, 7560, 83160, 1081080, 18378360, 349188840, 8031343320, 200783583000, 5822723907000, 180504441117000, ...

First differs from A306736 at n = 107. - Georg Fischer, Aug 13 2025

Links

• Amiram Eldar, Table of n, a(n) for n = 1..201

Crossrefs

Cf. A002110, A002182, A025487, A278908, A306736, A318278.

Programs

Mathematica

f[p_, e_] := 2^PrimeNu[e]; a[n_] := Times @@ (f @@@ FactorInteger[n]); s = {}; am = 0; Do[a1 = a[n]; If[a1 > am, am = a1; AppendTo[s, n]], {n, 1, 10^6}]; s

Formula

A278908(a(n)) = 2^(n-1).