A362627 Euler transform of sigma_n(n) (sum of n-th powers of divisors of n).
1, 1, 6, 34, 322, 3588, 52844, 900082, 18111465, 411941506, 10548286788, 298667744593, 9286665651198, 314077164671106, 11484692279345752, 451291302965764596, 18966834595501974235, 848853415894558707472, 40305029983754331855502, 2023571200162099967806430, 107109031661019664234558776
Offset: 0
Links
- N. J. A. Sloane, Transforms
- Eric Weisstein's World of Mathematics, Euler Transform
Programs
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Mathematica
a = Table[DivisorSigma[n, n], {n, 20}]; CoefficientList[Series[Product[1/(1 - x^m)^a[[m]], {m, 20}], {x, 0, 20}], x]
Formula
G.f.: Product_{k>=1} 1/(1 - x^k)^sigma(k,k).
a(n) = (1/n)*Sum_{k=1..n} a(n-k)*b(k) for n>1, a(0)=1, where b(k) = Sum_{d|k} d*sigma(d,d).