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

0,2

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.

Formula

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

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

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]

Crossrefs

Cf. A001694, A062762, A090699, A376092.

Sequence in context: A149120 A219151 A057819 * A129196 A119574 A006393

Adjacent sequences: A382787 A382788 A382789 * A382791 A382792 A382793

Keyword

nonn

Author

Amiram Eldar, Apr 05 2025

Status

approved