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A027860
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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).
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9
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0, 3, 256, 6075, 70656, 525300, 2861568, 12437115, 45414400, 144788634, 412896000, 1075797268, 2593575936, 5863302600, 12517805568, 25471460475, 49597544448, 93053764671, 168582124800, 296526859818, 506916761600, 846025507836, 1378885295616, 2203231674900
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OFFSET
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1,2
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COMMENTS
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It appears that this sequence is strictly increasing. - Jianing Song, Aug 05 2018
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REFERENCES
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"Number Theory I", vol. 49 of the Encyc. of Math. Sci.
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..2000
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FORMULA
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a(n) = (A013959(n) - A000594(n))/691. - Michel Marcus, Nov 12 2014
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MAPLE
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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
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MATHEMATICA
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{0}~Join~Array[(-RamanujanTau@ # + DivisorSigma[11, #])/691 &, 24] (* Michael De Vlieger, Aug 05 2018 *)
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PROG
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(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);
(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
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CROSSREFS
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Cf. A000594, A013959.
Similar sequences: A281788, A281876, A281928, A281956, A281979.
Sequence in context: A279653 A320023 A045824 * A059947 A203495 A051490
Adjacent sequences: A027857 A027858 A027859 * A027861 A027862 A027863
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KEYWORD
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nonn
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AUTHOR
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Bill Gosper
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EXTENSIONS
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More terms from Michel Marcus, Nov 12 2014
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STATUS
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approved
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