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A122162
Coefficient of q-series for constant term of Tate curve.
1
1, 23, 154, 647, 1876, 4802, 9948, 19975, 34903, 60648, 94502, 151298, 217504, 324844, 446404, 633351, 830298, 1144229, 1447250, 1931272, 2396352, 3105246, 3759604, 4821250, 5705001, 7155652, 8413300, 10373996, 11975000, 14696052
OFFSET
1,2
COMMENTS
If w6(n) = sum a(n) q^n and w4(n) = sum 5 sigma_3(n) q^n then the Tate elliptic curve is y^2 + xy = x^3 - w4(q)x - w6(q) If |q|<1 (for either real, complex, or p-adic values) and the resulting curve is nonsingular we have an elliptic curve. The parametrization is especially useful p-adically, behaving well in characteristic 2 or 3.
REFERENCES
Joseph H. Silverman, "Advanced Topics in the Arithmetic of Elliptic Curves", Springer, 1994
LINKS
H. D. Nguyen, D. Taggart, Mining the OEIS: Ten Experimental Conjectures, 2013. Mentions this sequence. - From N. J. A. Sloane, Mar 16 2014
FORMULA
a(n) = (5 sigma_3(n) + 7 sigma_5(n))/12, where sigma_3(n) is A001158, the sum of the cubes of the divisors of n and sigma_5(n) is A001160, the sum of the fifth powers of the divisors of n.
MATHEMATICA
Table[(5*DivisorSigma[3, n]+7*DivisorSigma[5, n])/12, {n, 30}] (* Harvey P. Dale, May 02 2018 *)
CROSSREFS
Sequence in context: A142044 A142935 A037068 * A122615 A231216 A133253
KEYWORD
nonn
AUTHOR
Gene Ward Smith, Aug 22 2006
STATUS
approved