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

1,2

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

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

Crossrefs

Cf. A000079, A000578, A115964, A359411.

Subsequence of A025487.

Similar sequences: A037992, A318278.

Sequence in context: A268471 A342598 A226524 * A115964 A245591 A247539

Adjacent sequences: A359409 A359410 A359411 * A359413 A359414 A359415

Keyword

nonn

Author

Amiram Eldar, Dec 30 2022

Status

approved