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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).

%I A027860 #35 Aug 21 2018 02:46:58
%S A027860 0,3,256,6075,70656,525300,2861568,12437115,45414400,144788634,
%T A027860 412896000,1075797268,2593575936,5863302600,12517805568,25471460475,
%U A027860 49597544448,93053764671,168582124800,296526859818,506916761600,846025507836,1378885295616,2203231674900
%N 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).
%C A027860 It appears that this sequence is strictly increasing. - _Jianing Song_, Aug 05 2018
%D A027860 "Number Theory I", vol. 49 of the Encyc. of Math. Sci.
%H A027860 Robert Israel, <a href="/A027860/b027860.txt">Table of n, a(n) for n = 1..2000</a>
%F A027860 a(n) = (A013959(n) - A000594(n))/691. - _Michel Marcus_, Nov 12 2014
%p A027860 N:= 100: # to get a(1) to a(N)
%p A027860 S:= series(q*mul((1-q^k)^24,k=1..N),q,N+1):
%p A027860 seq((-coeff(S,q,n) + add(d^11, d = numtheory:-divisors(n)))/691, n=1..N); # _Robert Israel_, Nov 12 2014
%t A027860 {0}~Join~Array[(-RamanujanTau@ # + DivisorSigma[11, #])/691 &, 24] (* _Michael De Vlieger_, Aug 05 2018 *)
%o A027860 (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);
%o A027860 (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
%o A027860 (Sage)
%o A027860 def A027860List(len):
%o A027860     r = list(delta_qexp(len+1))
%o A027860     return [(sigma(n, 11) - r[n])/691 for n in (1..len)]
%o A027860 A027860List(24) # _Peter Luschny_, Aug 20 2018
%Y A027860 Cf. A000594, A013959.
%Y A027860 Similar sequences: A281788, A281876, A281928, A281956, A281979.
%K A027860 nonn
%O A027860 1,2
%A A027860 _Bill Gosper_
%E A027860 More terms from _Michel Marcus_, Nov 12 2014