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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

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OFFSET

0,2

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

FORMULA

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

EXAMPLE

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

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 *)

PROG

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

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).

Sequence in context: A141284 A272812 A273207 * A072541 A141719 A098352

Adjacent sequences: A145151 A145152 A145153 * A145155 A145156 A145157

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 28 2009

STATUS

approved

URL: https://oeis.org/A145154

⇱ A145154 - OEIS