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

1,2

Links

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

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

Prog

(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*i<e-1), 3, 1)*(p-1)*p^(e+i-1)) )} \\ Andrew Howroyd, Jul 17 2018

Crossrefs

Cf. A046530, A087694, A062803.

Sequence in context: A373184 A097723 A187831 * A379776 A210468 A080950

Adjacent sequences: A087783 A087784 A087785 * A087787 A087788 A087789

Keyword

mult,nonn

Author

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

Extensions

More terms from John W. Layman, Oct 18 2003

Status

approved