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A217872
a(n) = sigma(n)^n.
12
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
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 01 2012
STATUS
approved