A283119
Expansion of exp( Sum_{n>=1} sigma(6*n)*x^n/n ) in powers of x.
Original entry on oeis.org
1, 12, 86, 469, 2141, 8594, 31247, 104945, 330094, 982284, 2786861, 7584060, 19893185, 50494558, 124437410, 298555264, 699017259, 1600364304, 3589048673, 7896510620, 17067607791, 36283650153, 75947406513, 156672628539, 318804641925, 640390347979
Offset: 0
G.f.: A(x) = 1 + 12*x + 86*x^2 + 469*x^3 + 2141*x^4 + 8594*x^5 + ...
log(A(x)) = 12*x + 28*x^2/2 + 39*x^3/3 + 60*x^4/4 + 72*x^5/5 + 91*x^6/6 + 96*x^7/7 + 124*x^8/8 + ... + sigma(6*n)*x^n/n + ...
Cf.
A224613 (sigma(6*n)),
A283164 (exp( Sum_{n>=1} -sigma(6*n)*x^n/n )).
-
Table[SeriesCoefficient[Product[(1 - x^(2 i))^4*(1 - x^(3 i))^3/((1 - x^i)^12*(1 - x^(6 i))), {i, n}], {x, 0, n}], {n, 0, 25}] (* Michael De Vlieger, Mar 01 2017 *)
A283120
Expansion of exp( Sum_{n>=1} sigma(8*n)*x^n/n ) in powers of x.
Original entry on oeis.org
1, 15, 128, 815, 4289, 19663, 81057, 306799, 1081986, 3594142, 11338690, 34193246, 99080387, 277046893, 750192227, 1973050940, 5053026949, 12628736331, 30859262181, 73849589786, 173333118663, 399528823032, 905418038792, 2019454523623, 4437187104779
Offset: 0
G.f.: A(x) = 1 + 15*x + 128*x^2 + 815*x^3 + 4289*x^4 + 19663*x^5 + ...
log(A(x)) = 15*x + 31*x^2/2 + 60*x^3/3 + 63*x^4/4 + 90*x^5/5 + 124*x^6/6 + 120*x^7/7 + 127*x^8/8 + ... + sigma(8*n)*x^n/n + ...
Cf.
A283122 (sigma(8*n)),
A283168 (exp( Sum_{n>=1} -sigma(8*n)*x^n/n )).
A283121
Expansion of exp( Sum_{n>=1} sigma(9*n)*x^n/n ) in powers of x.
Original entry on oeis.org
1, 13, 104, 633, 3224, 14404, 58151, 216294, 751582, 2464860, 7689669, 22961822, 65955677, 182985947, 492016590, 1285829996, 3274100475, 8139933477, 19795490575, 47165634583, 110259083454, 253208634687, 571880965638, 1271549402110, 2785836824325, 6019078365425
Offset: 0
G.f.: A(x) = 1 + 13*x + 104*x^2 + 633*x^3 + 3224*x^4 + 14404*x^5 + ...
log(A(x)) = 13*x + 39*x^2/2 + 40*x^3/3 + 91*x^4/4 + 78*x^5/5 + 120*x^6/6 + 104*x^7/7 + 195*x^8/8 + ... + sigma(9*n)*x^n/n + ...
Cf.
A283123 (sigma(9*n)),
A283169 (exp( Sum_{n>=1} -sigma(9*n)*x^n/n )).
A319362
a(n) = [x^n] exp(Sum_{k>=1} sigma(n*k)*x^k/k).
Original entry on oeis.org
1, 1, 8, 39, 385, 917, 31247, 22527, 1081986, 2464860, 50099635, 14931071, 19684696065, 394805109, 82267017929, 496514888157, 11386442827781, 284625019799, 3469798073972537, 7725084195239, 136470024990370842, 28400489198168457, 241211623942678951, 5776331152550399
Offset: 0
-
Table[SeriesCoefficient[Exp[Sum[DivisorSigma[1, n k] x^k/k, {k, 1, n}]], {x, 0, n}], {n, 0, 23}]
Showing 1-4 of 4 results.
Comments