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

1,2

Comments

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

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

Links

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

Formula

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)

Example

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 +...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A273232 A064546 A351591 * A067961 A104127 A043426

Adjacent sequences: A217869 A217870 A217871 * A217873 A217874 A217875

Keyword

nonn

Author

Paul D. Hanna, Nov 01 2012

Status

approved