A359412 Numbers with a record number of divisors that are both infinitary and exponential.

1, 8, 216, 27000, 9261000, 12326391000, 27081081027000, 110924107886592000, 544970142046826496000, 3737950204299182936064000, 45479640135708158783090688000, 1109202943269786284560798789632000, 33044264882950203203350756741926912000, 1673791149116076642859325881248823873536000

Offset: 1

Author

Amiram Eldar, Dec 30 2022

Keywords

• nonn

Comments

Indices of records in A359411.

a(2)-a(7) are the first 6 terms of A115964.

The first 15 terms are cubes. Are there noncubes in this sequence?

The corresponding record values are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, ... . Apparently, this sequence of records is the powers of 2 (A000079).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..15

Crossrefs

Cf. A000079, A000578, A115964, A359411.

Subsequence of A025487.

Similar sequences: A037992, A318278.

Programs

Mathematica

s[n_] := DivisorSum[n, 1 &, BitAnd[n, #] == # &]; f[p_, e_] := s[e]; 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