

A273488


Number of triples (x,y,z) with x,y,z in the set {0,...,n1} such that x + y + z is a cube and x^3 + 5*y^3 + 24*z^3 == 2 (mod n).


2



1, 2, 1, 1, 2, 5, 5, 3, 6, 6, 7, 2, 13, 8, 12, 10, 17, 2, 15, 9, 18, 24, 12, 8, 12, 23, 15, 11, 21, 25, 30, 14, 29, 27, 23, 25, 34, 29, 42, 19, 42, 35, 57, 16, 69, 45, 41, 23, 45, 43, 43, 34, 60, 77, 52, 23, 53, 64, 74, 33
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OFFSET

1,2


COMMENTS

Conjecture: For any positive integer n, the set {x^3 + 5*y^3 + 24*z^3: x,y,z = 0,...,n1 and x + y + z is a cube} contains a complete system of residues modulo n.
See also A273287 for a similar conjecture.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..350


EXAMPLE

a(2) = 2 since 0^3 + 5*0^3 + 24*0^3 == 2 (mod 2) with 0 + 0 + 0 = 0^3, and 0^3 + 5*0^3 + 24*1^3 == 2 (mod 2) with 0 + 0 + 1 = 1^3.
a(3) = 1 since 0^3 + 5*1^3 + 24*0^3 == 2 (mod 3) with 0 + 1 + 0 = 1^3.
a(4) = 1 since 3^3 + 5*3^3 + 24*2^3 == 2 (mod 4) with 3 + 3 + 2 = 2^3.


MATHEMATICA

CQ[n_]:=CQ[n]=IntegerQ[n^(1/3)]
In[2]:= Do[r=0; Do[If[Mod[x^3+5y^3+24z^32, n]==0&&CQ[x+y+z], r=r+1], {x, 0, n1}, {y, 0, n1}, {z, 0, n1}]; Print[n, " ", r]; Continue, {n, 1, 60}]


CROSSREFS

Cf. A000578, A273287.
Sequence in context: A289772 A283615 A216396 * A117848 A025242 A163982
Adjacent sequences: A273485 A273486 A273487 * A273489 A273490 A273491


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Aug 28 2016


STATUS

approved



