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

1,2

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.

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]

Crossrefs

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

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

Sequence in context: A107627 A017571 A016746 * A189268 A223673 A189621

Adjacent sequences: A384787 A384788 A384789 * A384791 A384792 A384793

Keyword

nonn

Author

Amiram Eldar, Jun 10 2025

Status

approved