A384790 Numbers with a record number of ways in which they can be expressed as b^2 * c^3, with b and c >= 1.

1, 64, 4096, 46656, 2985984, 191102976, 2176782336, 12230590464, 46656000000, 2985984000000, 34012224000000, 191102976000000, 2176782336000000, 139314069504000000, 351298031616000000, 4001504141376000000, 22483074023424000000, 256096265048064000000, 16390160963076096000000

Offset: 1

Author

Amiram Eldar, Jun 10 2025

Keywords

• nonn

Comments

Indices of records of A370256.

All the terms are powerful numbers since A370256(1) = 1 and A370256(n) = 0 if n is a nonpowerful number.

The corresponding record values are 1, 2, 3, 4, 6, 8, 9, 10, 12, 16, 18, 20, ... (see the link for more values).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..61.
• Amiram Eldar, n, a(n), A370256(a(n)) for n = 1..61.
• Index entries for sequences related to powerful numbers.

Crossrefs

Subsequence of A001694 and A025487 (i.e., of A181800).

Cf. A002182 (sixth root), A046055, A057523, A370256, A384791 (cubefull analog).

Programs

Mathematica

f[p_, e_] := Floor[(e + 2)/2] - Floor[(e + 2)/3]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; With[{lps = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {, }][[;; , 2]]}, sm = -1; seq = {}; Do[s1 = s[lps[[i]]]; If[s1 > sm, sm = s1; AppendTo[seq, lps[[i]]]], {i, 1, Length[lps]}]; seq]