|
| |
|
|
A087786
|
|
a(n) = number of solutions to x^3 - y^3 == 0 (mod n).
|
|
6
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
|
|
|
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
|
|
|
|
KEYWORD
|
mult,nonn
|
|
|
AUTHOR
|
Yuval Dekel (dekelyuval(AT)hotmail.com), Oct 06 2003
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
