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

1,1

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.

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A034503 A026557 A124052 * A104353 A001860 A199035

Adjacent sequences: A215637 A215638 A215639 * A215641 A215642 A215643

Keyword

nonn

Author

Arkadiusz Wesolowski, Aug 18 2012

Status

approved