A386786
a(n) = n^4*sigma_6(n).
Original entry on oeis.org
0, 1, 1040, 59130, 1065216, 9766250, 61495200, 282477650, 1090785280, 3491573931, 10156900000, 25937439242, 62986222080, 137858520410, 293776756000, 577478362500, 1116964192256, 2015993983970, 3631236888240, 6131066388122, 10403165760000, 16702903444500, 26974936811680
Offset: 0
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[0] cat [n^4*DivisorSigma(6, n): n in [1..35]]; // Vincenzo Librandi, Aug 03 2025
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Table[n^4*DivisorSigma[6, n], {n, 0, 30}]
nmax = 30; CoefficientList[Series[Sum[k^4*x^k*(1 + 1013*x^k + 47840*x^(2*k) + 455192*x^(3*k) + 1310354*x^(4*k) + 1310354*x^(5*k) + 455192*x^(6*k) + 47840*x^(7*k) + 1013*x^(8*k) + x^(9*k))/(1 - x^k)^11, {k, 1, nmax}], {x, 0, nmax}], x]
A386781
a(n) = n^3*sigma_7(n).
Original entry on oeis.org
0, 1, 1032, 59076, 1056832, 9765750, 60966432, 282475592, 1082196480, 3488379453, 10078254000, 25937425932, 62433407232, 137858494046, 291514810944, 576921447000, 1108169199616, 2015993905362, 3600007595496, 6131066264660, 10320757104000, 16687528072992, 26767423561824
Offset: 0
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[0] cat [n^3*DivisorSigma(7, n): n in [1..35]]; // Vincenzo Librandi, Aug 04 2025
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Table[n^3*DivisorSigma[7, n], {n, 0, 30}]
(* or *)
nmax = 30; CoefficientList[Series[Sum[k^10*x^k*(x^(2*k) + 4*x^k + 1)/(1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x]
(* or *)
terms = 30; E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}]; E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}]; E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}]; CoefficientList[Series[(3*E2[x]^3*E4[x]^2 + 5*E2[x]*E4[x]^3 - 9*E2[x]^2*E4[x]*E6[x] - 3*E4[x]^2*E6[x] + 4*E2[x]*E6[x]^2)/3456, {x, 0, terms}], x]
A386782
a(n) = n^3*sigma_8(n).
Original entry on oeis.org
0, 1, 2056, 177174, 4210752, 48828250, 364269744, 1977327086, 8623620608, 31385843307, 100390882000, 285311671942, 746035774848, 1792160396234, 4065384488816, 8651096365500, 17661175009280, 34271896312546, 64529293839192, 116490258905078, 205603651344000, 350330949134964
Offset: 0
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[0] cat [n^3*DivisorSigma(8, n): n in [1..35]]; // Vincenzo Librandi, Aug 04 2025
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Table[n^3*DivisorSigma[8, n], {n, 0, 30}]
nmax = 30; CoefficientList[Series[Sum[k^11*x^k*(x^(2*k) + 4*x^k + 1)/(1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x]
Showing 1-3 of 3 results.