|
Search: id:A035179
|
|
|
| A035179 |
|
Sum over divisors d of n of kronecker(-11,d). |
|
+0
2
|
|
| 1, 0, 2, 1, 2, 0, 0, 0, 3, 0, 1, 2, 0, 0, 4, 1, 0, 0, 0, 2, 0, 0, 2, 0, 3, 0, 4, 0, 0, 0, 2, 0, 2, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 1, 6, 0, 2, 2, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 4, 0, 0, 0, 1, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 2, 5, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 0, 2, 0, 3, 3, 0, 0, 2, 0, 0
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
Half of the number of integer solutions to x^2+xy+3y^2=n. - Michael Somos Jun 05 2005
|
|
REFERENCES
|
H. McKean and V. Moll, Elliptic Curves, Cambridge University Press, 1997, page 202. MR1471703 (98g:14032)
|
|
FORMULA
|
a(n) is multiplicative with a(11^e) = 1, a(p^e) = (1+(-1)^e)/2 if p == 2,6,7,8,10 (mod 11), a(p^e) = e+1 if p == 1,3,4,5,9 (mod 11) . - Michael Somos Jan 29 2007
Moebius transform is period 11 sequence [ 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 0, ...]. - Michael Somos Jan 29 2007
G.f.: Sum_{k>0} kronecker(-11,n)*x^n/(1-x^n) . - Michael Somos Jan 29 2007
|
|
PROGRAM
|
(PARI) a(n)=if(n<1, 0, qfrep([2, 1; 1, 6], n, 1)[n]) /* Michael Somos Jun 05 2005 */
(PARI) a(n)=if(n<1, 0, direuler(p=2, n, 1/(1-X)/(1-kronecker(-11, p)*X))[n]) /* Michael Somos Jun 05 2005 */
(PARI) {a(n)=if(n<1, 0, sumdiv(n, d, kronecker(-11, d)))}
|
|
CROSSREFS
|
Adjacent sequences: A035176 A035177 A035178 this_sequence A035180 A035181 A035182
Sequence in context: A065040 A057595 A035201 this_sequence A035161 A035186 A035194
|
|
KEYWORD
|
nonn,mult
|
|
AUTHOR
|
njas
|
|
|
Search completed in 0.002 seconds
|
