A215640 - OEIS

%I #25 Apr 06 2024 07:54:00

%S 3,12,28,168,360,1170,9360,19344,232128,3249792,6604416,20321280,

%T 104993280,1889879040,37797580800,907141939200,1828682956800,

%U 54860488704000,1755535638528000,12508191424512000,37837279059148800,1437816604247654400,60388297378401484800

%N Sum of divisors of colossally abundant numbers.

%H Amiram Eldar, <a href="/A215640/b215640.txt">Table of n, a(n) for n = 1..382</a> (terms 1..128 from Arkadiusz Wesolowski)

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RiemannHypothesis.html">Riemann Hypothesis</a>.

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

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

%t 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_ *)

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

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Aug 18 2012