A382790 a(n) is the (2^n)-th powerful number.

1, 4, 9, 32, 121, 392, 1352, 5000, 18432, 69192, 265837, 1024144, 3968064, 15523600, 60972500, 240413400, 950612224, 3767130288, 14959246864, 59495990724, 236902199076, 944193944097, 3765996039168, 15029799230264, 60010866324576, 239700225078125, 957712290743329

Offset: 0

Author

Amiram Eldar, Apr 05 2025

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..51 (terms 0..43 from Amiram Eldar)
• Index entries for sequences related to powerful numbers.

Crossrefs

Cf. A001694, A062762, A090699, A376092.

Programs

Mathematica

seq[max_] := Module[{p = Union@ Flatten@ Table[i^2*j^3, {j, 1, max^(1/3)}, {i, 1, Sqrt[max/j^3]}]}, p[[2^Range[0, Floor[Log2[Length[p]]]]]]]; seq[10^12]

Formula

a(n) = A001694(2^n).

a(n) ~ c * 4^n, where c = (zeta(3)/zeta(3/2))^2 = 1/A090699^2.