A078386 -id:A078386 - cp's OEIS frontend

A078387 Moebius's mu of numbers which can be written as sum of a positive square and a positive cube.

-1, -1, 0, 1, 0, -1, 0, 1, 0, -1, 1, 0, -1, -1, 0, 0, 0, 1, 0, 1, 0, 0, -1, 0, 0, 1, -1, 1, 0, -1, 0, -1, 1, 0, -1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, -1, 0, -1, 1, 1, 0, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, -1, -1, 0, -1, 0, 0, 1, -1, 0, -1, 0, -1, 0, 0, 0, 0, 1, 0, 0, -1, 0, -1, 0, 0, 0, -1, -1, 0, 1, 0, 0, -1, 1, -1

Offset: 1

Reinhard Zumkeller, Nov 25 2002

sign

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

Cf. A008683, A055394, A078386.

MoebiusMu[Select[Range[200], Length[Reduce[a^2 + b^3 == # && a > 0 && b > 0, {a, b}, Integers]] > 0 &]] (* Amiram Eldar, Mar 27 2025 *)

a(n) = A008683(A055394(n)).

A078388 Arithmetic derivative of numbers which can be written as sum of a positive square and a positive cube.

Original entry on oeis.org

1, 1, 6, 7, 16, 1, 44, 15, 32, 1, 14, 60, 1, 1, 48, 45, 56, 22, 51, 18, 72, 156, 1, 80, 176, 43, 1, 20, 140, 1, 216, 1, 63, 165, 1, 448, 46, 69, 50, 34, 152, 185, 236, 30, 168, 129, 123, 151, 62, 42, 216, 252, 1, 284, 105, 432, 38, 284, 1, 240, 115, 356, 1, 1, 211, 456

Offset: 1

Reinhard Zumkeller, Nov 25 2002

nonn

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

Cf. A003415, A055394, A078386.

ad[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); ad /@ Select[Range[300], Length[Reduce[a^2 + b^3 == # && a > 0 && b > 0, {a, b}, Integers]] > 0 &] (* Amiram Eldar, Mar 27 2025 *)

a(n) = A003415(A055394(n)). - Amiram Eldar, Mar 27 2025

cp's OEIS Frontend

A078387 Moebius's mu of numbers which can be written as sum of a positive square and a positive cube.

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