A066647 Squares of the form a^2 + b^3 with a, b > 0.

9, 36, 100, 196, 225, 289, 441, 576, 784, 841, 1225, 1296, 1764, 1849, 2025, 2304, 3025, 3249, 3600, 3844, 3969, 4356, 5776, 6084, 6400, 6561, 8100, 8281, 9801, 11025, 12544, 13924, 14161, 14400, 15129, 16129, 16641, 17424, 18496, 19600, 19881, 20449, 21609, 23409

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A070745(n)^2. - Amiram Eldar, Mar 20 2025

Example

29^2 = a(9) = 841 = 625 + 216 = 25^2 + 6^3.

Mathematica

q[n_] := Length[Reduce[a^2 + b^3 == n && a > 0 && b > 0, {a, b}, Integers]] > 0; Select[Range[140]^2, q] (* Amiram Eldar, Mar 20 2025 *)

Crossrefs

Cf. A055394, A066648, A070745.

Sequence in context: A027602 A231670 A134537 * A187607 A231674 A085037

Adjacent sequences: A066644 A066645 A066646 * A066648 A066649 A066650

Keyword

nonn

Author

Reinhard Zumkeller, Dec 17 2001

Status

approved