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Numbers n such that n | sigma_3(n) + sigma_2(n) + sigma_1(n) + sigma_0(n).
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%I #11 Nov 25 2016 05:28:46

%S 1,4,5,6,9,14,42,69,138,428,2772,3243,3306,4830,7882,24720,49710,

%T 53403,314184,1351280,1847772,27247596,31525032,41113416,41590824,

%U 42844894,44193564,47287104,95962560,104935384,124365885,211756464,569983507

%N Numbers n such that n | sigma_3(n) + sigma_2(n) + sigma_1(n) + sigma_0(n).

%C sigma_0(n) is the number of divisors of n (A000005).

%C sigma_1(n) is the sum of the divisors of n [same as sigma(n)] (A000203).

%C sigma_2(n) is the sum of the squares of the divisors of n (A001157).

%C sigma_3(n) is the sum of the cubes of the divisors of n (A001158).

%t Do[ If[ Mod[ DivisorSigma[3, n] + DivisorSigma[2, n] + DivisorSigma[1, n] + DivisorSigma[0, n], n] == 0, Print[n]], {n, 1, 6.6 10^6}]

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Nov 11 2000

%E a(22)-a(33) from _Donovan Johnson_, Mar 06 2011