|
| |
|
|
A002070
|
|
Coefficient of x^p (p = n-th prime) in x * Product_{k=1..inf} (1-x^k)^2*(1-x^11k)^2.
(Formerly M0072 N0024)
|
|
3
| |
|
|
-2, -1, 1, -2, 1, 4, -2, 0, -1, 0, 7, 3, -8, -6, 8, -6, 5, 12, -7, -3, 4, -10, -6, 15, -7, 2, -16, 18, 10, 9, 8, -18, -7, 10, -10, 2, -7, 4, -12, -6, -15, 7, 17, 4, -2, 0, 12, 19, 18, 15, 24, -30, -8, -23, -2, 14, 10, -28, -2, -18, 4, 24, 8, 12, -1, 13, 7, -22, 28, 30, -21, -20, -17, -26, -5, -1, -15, -2
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Form the infinite product x*[(1-x)*(1-x^11)*(1-x^2)*(1-x^22)*(1-x^3)*(1-x^33)*(1-x^4)*(1-x^44)*...]^2 and take the coefficients of x^2, x^3, x^5, x^7, x^11, x^13, x^17, x^19, ...
The primes p where A006571(p) == 0 (mod p) are called supersingular for the elliptic curve "11a3" and are given by sequence A006962. - Michael Somos Dec 25 2010
|
|
|
REFERENCES
| Shimura, Goro; A reciprocity law in non-solvable extensions. J. Reine Angew. Math. 221 1966 209-220.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| N. J. A. Sloane, Table of n, a(n) for n = 1..1229
|
|
|
MATHEMATICA
| a[ n_] := If[ n < 1, 0, With[ {m = Prime @ n}, SeriesCoefficient[ q (Product[ (1 - q^(11 k)), {k, Ceiling[m/11]}]Product[ 1 - q^k, {k, m}])^2, {q, 0, m}]]] (* Michael Somos Jul 04 2011 *)
|
|
|
CROSSREFS
| Cf. A006571 (all coefficients). A006962.
Sequence in context: A165585 A082506 A053000 * A106052 A050473 A057593
Adjacent sequences: A002067 A002068 A002069 * A002071 A002072 A002073
|
|
|
KEYWORD
| sign,easy,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
