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

1,2

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, ...

Links

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

Formula

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

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

Crossrefs

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

Sequence in context: A139033 A001044 A306736 * A346292 A086879 A372241

Adjacent sequences: A307842 A307843 A307844 * A307846 A307847 A307848

Keyword

nonn

Author

Amiram Eldar, May 01 2019

Status

approved