A377709 Numbers that have a record number of infinitary divisors that are powerful (A001694).

1, 4, 8, 36, 72, 128, 216, 1152, 3456, 27000, 28800, 86400, 279936, 432000, 4233600, 6998400, 21168000, 34992000, 148176000, 342921600, 1714608000, 8957952000, 12002256000, 197222256000, 207467568000, 438939648000, 1071630000000, 1452272976000, 3072577536000, 7501410000000

Offset: 1

Author

Amiram Eldar, Nov 04 2024

Keywords

• nonn

Comments

Indices of records in A360721.

The corresponding record values are 1, 2, 3, 4, 6, 7, 9, 14, 21, 27, 28, 42, 49, 63, 84, 98, ... (see the link for more values).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..117
• Amiram Eldar, Table of n, a(n), A360721(a(n)) for n = 1..117

Crossrefs

Cf. A001694, A037445, A360721.

Subsequence of A025487.

Programs

Mathematica

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