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Exponential unitary highly composite numbers: where the number of exponential unitary divisors (A278908) increases to a record.
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%I #13 May 07 2019 15:45:29

%S 1,4,36,576,14400,705600,57153600,6915585600,1168733966400,

%T 337764116289600,121932845980545600,64502475523708622400,

%U 40314047202317889000000,33904113697149344649000000,32581853262960520207689000000,44604557116992952164326241000000,74980260513665152588232411121000000

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

%C Subsequence of A025487.

%C 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, ...

%H Amiram Eldar, <a href="/A307845/b307845.txt">Table of n, a(n) for n = 1..201</a>

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

%t 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

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

%K nonn

%O 1,2

%A _Amiram Eldar_, May 01 2019