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A217872 a(n) = sigma(n)^n.

%I A217872 #31 Nov 16 2020 03:07:27
%S A217872 1,9,64,2401,7776,2985984,2097152,2562890625,10604499373,
%T A217872 3570467226624,743008370688,232218265089212416,793714773254144,
%U A217872 21035720123168587776,504857282956046106624,727423121747185263828481,2185911559738696531968,43567528752021332753202420081
%N A217872 a(n) = sigma(n)^n.
%C A217872 Here sigma(n) = A000203(n) is the sum of the divisors of n.
%C A217872 Compare to A023887(n) = sigma(n,n).
%H A217872 Paul D. Hanna, <a href="/A217872/b217872.txt">Table of n, a(n) for n = 1..200</a>
%F A217872 Logarithmic derivative of A156217.
%F A217872 From _Amiram Eldar_, Nov 16 2020: (Start)
%F A217872 Sum_{n>=1} 1/a(n) = A215140.
%F A217872 Sum_{n>=1} (-1)^(n+1)/a(n) = A215141. (End)
%e A217872 L.g.f.: L(x) = x + 3^2*x^2/2 + 4^3*x^3/3 + 7^4*x^4/4 + 6^5*x^5/5 + 12^6*x^6/6 +...
%e A217872 where exponentiation yields the g.f. of A156217:
%e A217872 exp(L(x)) = 1 + x + 5*x^2 + 26*x^3 + 634*x^4 + 2273*x^5 + 502568*x^6 +...
%t A217872 Table[DivisorSigma[1, n]^n, {n, 1, 20}] (* _Amiram Eldar_, Nov 16 2020 *)
%o A217872 (PARI) {a(n)=sigma(n)^n}
%o A217872 for(n=1,20,print1(a(n),", "))
%Y A217872 Cf. A000203, A023887, A156217, A215140, A215141.
%K A217872 nonn
%O A217872 1,2
%A A217872 _Paul D. Hanna_, Nov 01 2012