A087786 a(n) = number of solutions to x^3 - y^3 == 0 (mod n).

1, 2, 3, 6, 5, 6, 19, 20, 27, 10, 11, 18, 37, 38, 15, 40, 17, 54, 55, 30, 57, 22, 23, 60, 45, 74, 135, 114, 29, 30, 91, 112, 33, 34, 95, 162, 109, 110, 111, 100, 41, 114, 127, 66, 135, 46, 47, 120, 175, 90, 51, 222, 53, 270, 55, 380, 165, 58, 59, 90, 181, 182, 513, 352, 185

Offset: 1

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Oct 06 2003

Keywords

• mult
• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A046530, A087694, A062803.

Programs

PARI

a(n)={my(v=vector(n)); for(i=0, n-1, v[i^3%n + 1]++); sum(i=0, n-1, v[i+1]^2)} \\ Andrew Howroyd, Jul 17 2018

PARI

a(n)={my(f=factor(n)); prod(i=1, #f~, my(p=f[i,1], e=f[i,2]); p^(2*(2*e\3)) + sum(i=0, (e-1)\3, if(p%3==1 || (p==3&&3*iAndrew Howroyd, Jul 17 2018

Formula

Multiplicative with a(p^e) = p^(2*floor(2*e/3)) + Sum_{i=0..floor((e-1)/3)} k*(p-1)*p^(e+i-1) where k = 3 if (p = 3 and 3*i+1 = e) or (p mod 3 = 1) otherwise k = 1. - Andrew Howroyd, Jul 17 2018

Extensions

More terms from John W. Layman, Oct 18 2003