A027860 a(n) = (-tau(n) + sigma_11(n)) / 691, where tau is Ramanujan's tau (A000594), sigma_11(n) = Sum_{ d divides n } d^11 (A013959).

0, 3, 256, 6075, 70656, 525300, 2861568, 12437115, 45414400, 144788634, 412896000, 1075797268, 2593575936, 5863302600, 12517805568, 25471460475, 49597544448, 93053764671, 168582124800, 296526859818, 506916761600, 846025507836, 1378885295616, 2203231674900

Offset: 1

Author

Bill Gosper

Keywords

• nonn

Comments

It appears that this sequence is strictly increasing. - Jianing Song, Aug 05 2018

References

• "Number Theory I", vol. 49 of the Encyc. of Math. Sci.

Links

• Robert Israel, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000594, A013959.

Similar sequences: A281788, A281876, A281928, A281956, A281979.

Programs

Macsyma

(sum(n^11*q^n/(1-q^n), n,1,inf)-q*prod(1-q^n,n,1,inf)^24)/691; taylor(%,q,0,24);

Maple

N:= 100: # to get a(1) to a(N)
S:= series(q*mul((1-q^k)^24,k=1..N),q,N+1):
seq((-coeff(S,q,n) + add(d^11, d = numtheory:-divisors(n)))/691, n=1..N); # Robert Israel, Nov 12 2014

Mathematica

{0}~Join~Array[(-RamanujanTau@ # + DivisorSigma[11, #])/691 &, 24] (* Michael De Vlieger, Aug 05 2018 *)

PARI

a(n) = (sigma(n, 11) - polcoeff( x * eta(x + x * O(x^n))^24, n))/691; \\ for n>0; Michel Marcus, Nov 12 2014

Sage

def A027860List(len):
    r = list(delta_qexp(len+1))
    return [(sigma(n, 11) - r[n])/691 for n in (1..len)]
A027860List(24) # Peter Luschny, Aug 20 2018

Formula

a(n) = (A013959(n) - A000594(n))/691. - Michel Marcus, Nov 12 2014

Extensions

More terms from Michel Marcus, Nov 12 2014