A363330 Numbers with a record number of divisors that are both coreful and infinitary.

1, 8, 128, 216, 3456, 27000, 279936, 432000, 9261000, 34992000, 148176000, 8957952000, 12002256000, 197222256000, 3072577536000, 7501410000000, 15975002736000, 433297296432000, 1920360960000000, 4089600700416000, 9984376710000000, 35097081010992000, 2128789617370416000

Offset: 1

Author

Amiram Eldar, May 28 2023

Keywords

• nonn

Comments

Indices of records in A363329.

The corresponding record values are 1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 315, ... (see the link for more values).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..64
• Amiram Eldar, Table of n, a(n), A363329(a(n)) for n = 1..64

Crossrefs

Cf. A363329.

Subsequence of A025487.

Similar sequences: A005934, A037992.

Programs

Mathematica

f[p_, e_] := 2^DigitCount[e, 2, 1] - 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