A362853 Numbers with a record number of divisors that are both bi-unitary and exponential.

1, 8, 64, 216, 1728, 27000, 46656, 110592, 216000, 2985984, 5832000, 13824000, 74088000, 373248000, 2000376000, 4741632000, 46656000000, 98611128000, 128024064000, 2662500456000, 6311112192000, 16003008000000, 93329542656000, 170400029184000, 5489031744000000

Offset: 1

Author

Amiram Eldar, May 05 2023

Keywords

• nonn

Comments

Indices of records in A362852.

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

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).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..80
• Amiram Eldar, Table of n, a(n), A362852(a(n)) for n = 1..80

Crossrefs

Cf. A362852.

Subsequence of A025487.

Similar sequences: A293185, A318278.

Programs

Mathematica

f[p_, e_] := DivisorSigma[0, e] - If[OddQ[e], 0, 1]; d[1] = 1; d[n_] := Times @@ f @@@ FactorInteger[n];
v = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {, }][[;; , 2]];
seq = {}; dm = 0; Do[If[(dk = d[v[[k]]]) > dm, dm = dk; AppendTo[seq, v[[k]]]], {k, 1, Length[v]}]; seq