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%I A067313 #20 Aug 10 2020 13:19:14
%S A067313 1,10,130,135,147,150,228,250,350,364,410,444,492,876,891,945,1014,
%T A067313 1308,1372,1550,1690,1950,2050,2210,2373,2565,2850,3045,3050,3250,
%U A067313 3375,3876,4108,4185,4905,4995,5050,5070,5145,5330,5439,5481,6150,6250,6321,6615,6890,7514
%N A067313 Numbers k such that sigma_k(k)/k is an integer, where sigma_k(k) is the sum of the k-th powers of the divisors of k (A023887).
%H A067313 David A. Corneth, <a href="/A067313/b067313.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Amiram Eldar)
%e A067313 If k = 10, then sigma(10,10) = 1 + 1024 + 9765625 + 10000000000 = 1009766650 is divisible by k = 10.
%t A067313 Do[s=DivisorSigma[n, n]; If[IntegerQ[s/n], Print[n]], {n, 1, 10000}]
%t A067313 Select[Range[6500],Divisible[DivisorSigma[#,#],#]&] (* _Harvey P. Dale_, Feb 06 2019 *)
%o A067313 (PARI) isok(k) = !(sigma(k, k) % k); \\ _Michel Marcus_, Aug 10 2020
%o A067313 (PARI) is(n) = {my(d = divisors(n), v = vecsum(vector(#d - 1, i, Mod(d[i], n)^n))); lift(v)==0} \\ _David A. Corneth_, Aug 10 2020
%Y A067313 Cf. A023887.
%K A067313 nonn
%O A067313 1,2
%A A067313 _Labos Elemer_, Jan 14 2002

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