Original entry on oeis.org
1, 11, 113, 7103, 8778881, 2302890927539, 7289913993299309016859, 330513634706872709970497049176749987771, 52698433600606388974675914778280598904460888679269021907794061677149
Offset: 1
A207709(11) = 2 since A207709(113) = 3 is the next record value.
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lst = {}; h = k = n = 0; Do[While[n <= max, k++; h = h + 1/k; n = (h + Exp@h*Log@h)/DivisorSigma[1, k]]; AppendTo[lst, k], {max, 2, 4}]; Prepend[lst, 1]
A215640
Sum of divisors of colossally abundant numbers.
Original entry on oeis.org
3, 12, 28, 168, 360, 1170, 9360, 19344, 232128, 3249792, 6604416, 20321280, 104993280, 1889879040, 37797580800, 907141939200, 1828682956800, 54860488704000, 1755535638528000, 12508191424512000, 37837279059148800, 1437816604247654400, 60388297378401484800
Offset: 1
6 is the second colossally abundant number. Divisors of 6 are 1, 2, 3, 6, so a(2) = 1 + 2 + 3 + 6 = 12.
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lst1 = {2}; lst2 = {}; maxN = 23; p = 1; pFactor[f_List] := Module[{p = f[[1]], k = f[[2]]}, N[Log[(p^(k + 2) - 1)/(p^(k + 1) - 1)]/Log[p]] - 1]; f = {{2, 1}, {3, 0}}; primes = 1; x = Table[pFactor[f[[i]]], {i, primes + 1}]; For[n = 2, n <= maxN, n++, i = Position[x, Max[x]][[1, 1]]; AppendTo[lst1, f[[i, 1]]]; f[[i, 2]]++; If[i > primes, primes++; AppendTo[f, {Prime[i + 1], 0}]; AppendTo[x, pFactor[f[[-1]]]]]; x[[i]] = pFactor[f[[i]]]]; Do[p = p*lst1[[n]]; AppendTo[lst2, DivisorSigma[1, p]], {n, maxN}]; lst2 (* Most of the code is from T. D. Noe *)
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