%I #8 May 05 2023 12:54:08

%S 1,8,64,216,1728,27000,46656,110592,216000,2985984,5832000,13824000,

%T 74088000,373248000,2000376000,4741632000,46656000000,98611128000,

%U 128024064000,2662500456000,6311112192000,16003008000000,93329542656000,170400029184000,5489031744000000

%N Numbers with a record number of divisors that are both bi-unitary and exponential.

%C Indices of records in A362852.

%C The first 80 terms are cubes. Are there noncubes in this sequence?

%C The corresponding record values are 1, 2, 3, 4, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, ... (see the link for more values).

%H Amiram Eldar, <a href="/A362853/b362853.txt">Table of n, a(n) for n = 1..80</a>

%H Amiram Eldar, <a href="/A362853/a362853.txt">Table of n, a(n), A362852(a(n)) for n = 1..80</a>

%t f[p_, e_] := DivisorSigma[0, e] - If[OddQ[e], 0, 1]; d[1] = 1; d[n_] := Times @@ f @@@ FactorInteger[n];

%t v = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]];

%t seq = {}; dm = 0; Do[If[(dk = d[v[[k]]]) > dm, dm = dk; AppendTo[seq, v[[k]]]], {k, 1, Length[v]}]; seq

%Y Cf. A362852.

%Y Subsequence of A025487.

%Y Similar sequences: A293185, A318278.

%K nonn

%O 1,2

%A _Amiram Eldar_, May 05 2023