OFFSET
0,2
REFERENCES
B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 463 Entry 4(i).
LINKS
John Cannon, Table of n, a(n) for n = 0..5000
Shaun Cooper and Dongxi Ye, Level 14 AND 15 Analogues of Ramanujan's Elliptic Functions to Alternative Bases, preprint, 2015.
G. Nebe and N. J. A. Sloane, Home page for this lattice
FORMULA
a(n) = 6*b(n) where b(n) is multiplicative with a(0) = 1, b(5^e) = 1, b(p^e) = (p^(e+1) - 1) / (p - 1) otherwise. - Michael Somos, Feb 04 2006
G.f. 1 + 6 * (Sum_{k>0} k * x^k / (1 - x^k) - 5*k * x^(5*k) / (1 - x^(5*k))). - Michael Somos, Feb 04 2006
EXAMPLE
G.f. = 1 + 6*x + 18*x^2 + 24*x^3 + 42*x^4 + 6*x^5 + 72*x^6 + 48*x^7 + ...
G.f. = 1 + 6*q^2 + 18*q^4 + 24*q^6 + 42*q^8 + 6*q^10 + 72*q^12 + 48*q^14 + ...
MATHEMATICA
a[ n_] := If[ n < 1, Boole[ n == 0], 6 Sum[ If[ Mod[ d, 5] > 0, d, 0], {d, Divisors @ n }]]; (* Michael Somos, Jun 12 2014 *)
a[ n_] := SeriesCoefficient[ 1 + 6 Sum[ k x^k / (1 - x^k) - 5 k x^(5 k) / (1 - x^(5 k)), {k, n}], {x, 0, n}]; (* Michael Somos, Jun 12 2014 *)
PROG
(PARI) {a(n) = if( n<1, n==0, 6 * sumdiv(n, d, (d%5>0) * d))}; /* Michael Somos, Feb 04 2006 */
(PARI) {a(n) = my(G); if( n<0, 0, G = [ 2, 1, 0, 0; 1, 2, 1, 0; 0, 1, 4, 5; 0, 0, 5, 10]; polcoeff( 1 + 2 * x * Ser( qfrep( G, n, 1)), n))}; /* Michael Somos, Jun 12 2014 */
(Sage) ModularForms( Gamma0(5), 2, prec=70).0; # Michael Somos, Jun 12 2014
(Magma) Basis( ModularForms( Gamma0(5), 2), 70) [1]; /* Michael Somos, Jun 12 2014 */
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved