A377138 Powerful numbers that have more divisors than any smaller powerful number.

1, 4, 8, 16, 32, 36, 72, 144, 216, 288, 432, 576, 864, 900, 1728, 1800, 3600, 5400, 7200, 10800, 14400, 21600, 32400, 43200, 64800, 86400, 88200, 176400, 264600, 352800, 529200, 705600, 1058400, 1587600, 2116800, 3175200, 4233600, 6350400, 8467200, 10584000, 12700800

Offset: 1

Author

Amiram Eldar, Oct 17 2024

Keywords

• nonn

Comments

First differs from A283052 at n = 12.

Indices of records in A357669.

The corresponding record values are 1, 3, 4, 5, 6, 9, 12, 15, 16, 18, 20, 21, 24, 27, 28, 36, ... (see the link for more values).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..548
• Amiram Eldar, Table of n, a(n), A357669(a(n)) for n = 1..548

Crossrefs

Subsequence of A001694 and A025487.

Cf. A000005, A002182, A283052, A357669, A363194.

Programs

Mathematica

f[p_, e_] := If[e == 1, 1, e + 1]; d[1] = 1; d[n_] := Times @@ f @@@ FactorInteger[n]; With[{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]