A215140 -id:A215140 - cp's OEIS frontend

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

1, 9, 64, 2401, 7776, 2985984, 2097152, 2562890625, 10604499373, 3570467226624, 743008370688, 232218265089212416, 793714773254144, 21035720123168587776, 504857282956046106624, 727423121747185263828481, 2185911559738696531968, 43567528752021332753202420081

Offset: 1

Paul D. Hanna, Nov 01 2012

nonn

Here sigma(n) = A000203(n) is the sum of the divisors of n.

Compare to A023887(n) = sigma(n,n).

			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 +...
where exponentiation yields the g.f. of A156217:
exp(L(x)) = 1 + x + 5*x^2 + 26*x^3 + 634*x^4 + 2273*x^5 + 502568*x^6 +...

Paul D. Hanna, Table of n, a(n) for n = 1..200

Cf. A000203, A023887, A156217, A215140, A215141.

Table[DivisorSigma[1, n]^n, {n, 1, 20}] (* Amiram Eldar, Nov 16 2020 *)

{a(n)=sigma(n)^n}
for(n=1,20,print1(a(n),", "))

Logarithmic derivative of A156217.
From Amiram Eldar, Nov 16 2020: (Start)
Sum_{n>=1} 1/a(n) = A215140.
Sum_{n>=1} (-1)^(n+1)/a(n) = A215141. (End)

A215141 Decimal expansion of Sum_{n>=1} (-1)^(n+1) / sigma(n)^n.

Original entry on oeis.org

9, 0, 4, 2, 2, 6, 1, 3, 8, 2, 2, 8, 4, 3, 4, 5, 2, 1, 1, 4, 6, 2, 7, 4, 9, 6, 5, 6, 2, 5, 6, 5, 6, 2, 7, 3, 2, 8, 7, 5, 1, 8, 2, 8, 3, 4, 9, 0, 3, 8, 1, 7, 6, 7, 3, 5, 9, 9, 7, 9, 1, 0, 9, 8, 7, 5, 8, 3, 2, 8, 2, 4, 3, 4, 7, 8, 8, 1, 4, 3, 0, 3, 6, 0, 5, 6, 8

Offset: 0

Michel Lagneau, Aug 04 2012

			.90422613822843452114627...

G. C. Greubel, Table of n, a(n) for n = 0..5000

Cf. A000203, A215140.

RealDigits[N[Sum[((-1)^(n+1))/DivisorSigma[1,n]^n,{n,1,105}],105]][[1]]

suminf(n=1, (-1)^(n+1)/sigma(n)^n) \\ Michel Marcus, Apr 20 2018

cp's OEIS Frontend

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

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