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A045823 a(n) = sigma_3(2*n+1). 10
1, 28, 126, 344, 757, 1332, 2198, 3528, 4914, 6860, 9632, 12168, 15751, 20440, 24390, 29792, 37296, 43344, 50654, 61544, 68922, 79508, 95382, 103824, 117993, 137592, 148878, 167832, 192080, 205380, 226982, 260408, 276948, 300764, 340704, 357912 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

FORMULA

Expansion of q^(-1) * ( E_4(q) - 9 * E_4(q^2) + 8 * E_4(q^4) ) / 240 in powers of q^2. - Michael Somos, Nov 29 2007

Expansion of q^(-1) * (eta(q^2)^24 + eta(q)^16 * eta(q^4)^8) / (2 * eta(q)^8 * eta(q^2)^8) in powers of q^2. - Michael Somos, Nov 29 2007

a(n) = b(2*n+1) where b(n) is multiplicative and b(2^e) = 0^e, b(p^e) = ((p^3)^(e+1) - 1) / (p^3 - 1) if p>2. - Michael Somos, Nov 29 2007

G.f.: (theta_3(q)^8 - theta_4(q)^8) / (32*q) = Sum_{n>=0} sigma_3(2*n+1)*q^(2*n). - Paul D. Hanna, Jun 02 2018

EXAMPLE

q + 28*q^3 + 126*q^5 + 344*q^7 + 757*q^9 + 1332*q^11 + 2198*q^13 + ...

MAPLE

A045823 := proc(n)

    numtheory[sigma][3](2*n+1) ;

end proc:

seq(A045823(n), n=0..30) ; # R. J. Mathar, Nov 25 2018

MATHEMATICA

DivisorSigma[3, Range[1, 75, 2]] (* Harvey P. Dale, Jan 11 2015 *)

PROG

(PARI) {a(n) = if( n<0, 0, sigma(2 * n + 1, 3))} /* Michael Somos, Nov 29 2007 */

(PARI) {a(n) = local(A); if( n<0, 0, n *= 2; A = x * O(x^n); polcoeff( (eta(x^2 + A)^24 + eta(x + A)^16 * eta(x^4 + A)^8) / (2 * eta(x + A)^8 * eta(x^2 + A)^8), n))} /* Michael Somos, Nov 29 2007 */

(MAGMA) [DivisorSigma(3, 2*n+1): n in [0..40]]; // Vincenzo Librandi, Jun 02 2019

CROSSREFS

A045819/2.

Bisection of A001158. Cf. A008438.

Sequence in context: A232403 A219851 A320885 * A327750 A044360 A044741

Adjacent sequences:  A045820 A045821 A045822 * A045824 A045825 A045826

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Benoit Cloitre, Apr 12 2003

STATUS

approved

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Last modified November 21 22:40 EST 2019. Contains 329383 sequences. (Running on oeis4.)