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%I #16 Feb 27 2018 08:43:25
%S 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,
%T 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,
%U 16,24,8,32,16,32,16,16,8,48
%N Coefficients in expansion of Eisenstein series E_1.
%H Antti Karttunen, <a href="/A145154/b145154.txt">Table of n, a(n) for n = 0..10000</a>
%H M. Kaneko and D. Zagier, <a href="http://www2.math.kyushu-u.ac.jp/~mkaneko/papers/atkin.pdf">Supersingular j-invariants, hypergeometric series and Atkin's orthogonal polynomials</a>, pp. 97-126 of D. A. Buell and J. T. Teitelbaum, eds., Computational Perspectives on Number Theory, Amer. Math. Soc., 1998
%F a(0) = 1; for n >= 1, a(n) = 4*A000005(n). [After the PARI-program of _Michael Somos_.] - _Antti Karttunen_, May 25 2017
%e 1 + 4*q + 8*q^2 + 8*q^3 + 12*q^4 + 8*q^5 + 16*q^6 + 8*q^7 + 16*q^8 + ...
%p 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);
%t terms = 61; CoefficientList[1+4*Sum[x^k/(1-x^k), {k, 1, terms}]+O[x]^terms, x] (* _Jean-François Alcover_, Feb 27 2018 *)
%o (PARI) {a(n) = if( n<1, n==0, 4 * numdiv(n))} /* _Michael Somos_, Jul 04 2011 */
%Y 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).
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Feb 28 2009
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