A078393 Squarefree numbers which can be written as sum of a positive square and a positive cube.

2, 5, 10, 17, 26, 31, 33, 37, 43, 57, 65, 73, 82, 89, 91, 101, 113, 122, 127, 129, 134, 141, 145, 161, 170, 174, 177, 185, 197, 206, 217, 223, 226, 233, 241, 246, 257, 265, 269, 283, 290, 321, 337, 347, 353, 359, 362, 379, 381, 385, 401, 407, 427, 442, 443

Offset

1,1

Links

Table of n, a(n) for n=1..55.

Example

7*13 = 91 = 8^2 + 3^3, therefore 91 is a term.

Mathematica

spspcQ[{a_, b_}]:=AllTrue[{Sqrt[a], Surd[b, 3]}, IntegerQ]||AllTrue[{Sqrt[ b], Surd[ a, 3]}, IntegerQ]; Select[Range[500], SquareFreeQ[#] && Length[ Select[IntegerPartitions[#, {2}], spspcQ]]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 13 2019 *)

Crossrefs

Cf. A005117, A066649.

Sequence in context: A340039 A003192 A018682 * A340045 A100292 A078325

Adjacent sequences: A078390 A078391 A078392 * A078394 A078395 A078396

Keyword

nonn

Author

Reinhard Zumkeller, Nov 25 2002

Status

approved