A215640 Sum of divisors of colossally abundant numbers.

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

Author

Arkadiusz Wesolowski, Aug 18 2012

Keywords

• nonn

Examples

			6 is the second colossally abundant number. Divisors of 6 are 1, 2, 3, 6, so a(2) = 1 + 2 + 3 + 6 = 12.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..382 (terms 1..128 from Arkadiusz Wesolowski)
• Eric Weisstein's World of Mathematics, Riemann Hypothesis.

Crossrefs

Cf. A000203, A004490, A058209, A080130, A207709.

Programs

Mathematica

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 *)

Formula

a(n) = A000203(A004490(n)).