A340038 Numbers that are the sum of a square s and a cube t such that 0 < s <= t.

2, 9, 12, 28, 31, 36, 43, 52, 65, 68, 73, 80, 89, 100, 113, 126, 128, 129, 134, 141, 150, 161, 174, 189, 206, 217, 220, 225, 232, 241, 246, 252, 265, 280, 297, 316, 337, 344, 347, 352, 359, 360, 368, 379, 385, 392, 407, 412, 424, 443, 464, 487, 512, 513, 516, 521, 528, 537, 539

Offset

1,1

Links

Table of n, a(n) for n=1..59.

Example

9 is in the sequence since 1^2 + 2^3 = 1 + 8 = 9, with 0 < 1 <= 8.

Mathematica

Table[If[Sum[(Floor[i^(1/2)] - Floor[(i - 1)^(1/2)]) (Floor[(n - i)^(1/3)] - Floor[(n - i - 1)^(1/3)]), {i, Floor[n/2]}] > 0, n, {}], {n, 600}] // Flatten
stQ[n_]:=Count[IntegerPartitions[n, {2}], _?(AllTrue[{Surd[#[[1]], 3], Sqrt[#[[2]]]}, IntegerQ]&)] > 0; Select[Range[600], stQ] (* Harvey P. Dale, Aug 22 2022 *)

Crossrefs

Cf. A010052, A010057.

Sequence in context: A347496 A304797 A337360 * A178312 A347495 A253608

Adjacent sequences: A340035 A340036 A340037 * A340039 A340040 A340041

Keyword

nonn

Author

Wesley Ivan Hurt, Dec 26 2020

Status

approved