A145154 Coefficients in expansion of Eisenstein series E_1.

1, 4, 8, 8, 12, 8, 16, 8, 16, 12, 16, 8, 24, 8, 16, 16, 20, 8, 24, 8, 24, 16, 16, 8, 32, 12, 16, 16, 24, 8, 32, 8, 24, 16, 16, 16, 36, 8, 16, 16, 32, 8, 32, 8, 24, 24, 16, 8, 40, 12, 24, 16, 24, 8, 32, 16, 32, 16, 16, 8, 48

Offset: 0

Author

N. J. A. Sloane, Feb 28 2009

Keywords

• nonn

Examples

			1 + 4*q + 8*q^2 + 8*q^3 + 12*q^4 + 8*q^5 + 16*q^6 + 8*q^7 + 16*q^8 + ...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10000
• M. Kaneko and D. Zagier, Supersingular j-invariants, hypergeometric series and Atkin's orthogonal polynomials, pp. 97-126 of D. A. Buell and J. T. Teitelbaum, eds., Computational Perspectives on Number Theory, Amer. Math. Soc., 1998

Crossrefs

Cf. A000005, A006352 (E_2), A004009 (E_4), A013973 (E_6), A008410 (E_8), A013974 (E_10), A029828 (E_12), A058550 (E_14), A029829 (E_16), A029830 (E_20), A029831 (E_24).

Programs

Maple

with(numtheory); E:=proc(k) series(1-(2*k/bernoulli(k))*add( sigma[k-1](n)*q^n, n=1..60),q,61); end; E(1);

Mathematica

terms = 61; CoefficientList[1+4*Sum[x^k/(1-x^k), {k, 1, terms}]+O[x]^terms, x] (* Jean-François Alcover, Feb 27 2018 *)

PARI

{a(n) = if( n<1, n==0, 4 * numdiv(n))} /* Michael Somos, Jul 04 2011 */

Formula

a(0) = 1; for n >= 1, a(n) = 4*A000005(n). [After the PARI-program of Michael Somos.] - Antti Karttunen, May 25 2017