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A215640 Sum of divisors of colossally abundant numbers. 2
3, 12, 28, 168, 360, 1170, 9360, 19344, 232128, 3249792, 6604416, 20321280, 104993280, 1889879040, 37797580800, 907141939200, 1828682956800, 54860488704000, 1755535638528000, 12508191424512000, 37837279059148800, 1437816604247654400, 60388297378401484800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..128

Eric W. Weisstein, MathWorld: 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. 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

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Last modified June 21 00:40 EDT 2021. Contains 345329 sequences. (Running on oeis4.)