A273287 Number of triples (x,y,z) with x,y,z in the set {0,...,n-1} such that x*y*z is a cube and x^3 + 2*y^3 + 3*z^3 == 7 (mod n).

1, 4, 7, 10, 14, 18, 1, 22, 27, 29, 34, 37, 35, 7, 47, 46, 54, 56, 44, 60, 17, 71, 71, 72, 76, 60, 80, 15, 92, 93, 81, 98, 104, 109, 25, 115, 118, 90, 91, 121, 129, 33, 114, 142, 135, 142, 145, 147, 22, 153, 163, 121, 168, 176, 174, 29, 135, 182, 185, 184

Offset

1,2

Comments

Conjecture: For any positive integer n, the set {x^3 + 2*y^3 + 3*z^3: x,y,z = 0,...,n-1 and x*y*z is a cube} contains a complete system of residues modulo n.

See also A273488 for a similar conjecture.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..300

Example

a(2) = 4 since 0^3 + 2*0^3 + 3*1^3 == 7 (mod 2) with 0*0*1 = 0^3, 0^3 + 2*1^3 + 3*1^3 == 7 (mod 2) with 0*1*1 = 0^3, 1^3 + 2*0^3 + 3*0^3 == 7 (mod 2) with 1*0*0 = 0^3, and 1^3 + 2*1^3 + 3*0^3 == 7 (mod 2) with 1*1*0 = 0^3.
a(7) = 1 since 0^3 + 2*0^3 + 3*0^3 == 7 (mod 7) with 0*0*0 = 0^3.

Mathematica

CQ[n_]:=CQ[n]=IntegerQ[n^(1/3)]
Do[r=0; Do[If[Mod[x^3+2y^3+3z^3-7, n]==0&&CQ[x*y*z], r=r+1], {x, 0, n-1}, {y, 0, n-1}, {z, 0, n-1}]; Print[n, " ", r]; Continue, {n, 1, 60}]

Crossrefs

Cf. A000578, A273488.

Sequence in context: A310690 A310691 A161187 * A310692 A300306 A310693

Adjacent sequences: A273284 A273285 A273286 * A273288 A273289 A273290

Keyword

nonn

Author

Zhi-Wei Sun, Aug 28 2016

Status

approved