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%I #30 Jun 17 2019 13:51:23
%S 1,2,2,4,2,9,2,14,11,23,2,83,2,73,108,202,2,546,2,905,780,1037,2,5553,
%T 627,4111,6644,12647,2,40605,2,49682,59172,65555,18028,382424,2,
%U 262165,531612,869675,2,2706581,2,3147083,5180382,4194329,2,27246533,117651
%N a(n) = Sum_{d|n} (n/d)^(d-1).
%H Seiichi Manyama, <a href="/A087909/b087909.txt">Table of n, a(n) for n = 1..6290</a>
%F G.f.: Sum_{k>0} x^k/(1-k*x^k).
%F From _Seiichi Manyama_, Jun 17 2019: (Start)
%F L.g.f.: -log(Product_{k>=1} (1 - k*x^k)^(1/k^2)) = Sum_{k>=1} a(k)*x^k/k.
%F a(p) = 2 for prime p. (End)
%t a[n_]:= DivisorSum[n, (n/#)^(#-1) &]; Array[a, 30] (* _G. C. Greubel_, May 16 2018 *)
%o (PARI) a(n)=sumdiv(n, d, d^(n/d-1) ); /* _Joerg Arndt_, Oct 07 2012 */
%o (PARI) N=66; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-k*x^k)^(1/k^2))))) \\ _Seiichi Manyama_, Jun 17 2019
%Y Cf. A055225, A078308.
%K nonn,look
%O 1,2
%A _Vladeta Jovovic_, Oct 15 2003
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