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%I #19 Sep 08 2022 08:46:23
%S 1,10,84,1092,15630,284700,5764808,134744072,3486961557,100097666500,
%T 3138428376732,107019534520152,3937376385699302,155577590681061500,
%U 6568408813691796120,295152408847700721680,14063084452067724991026,708238048886859220660710
%N a(n) = n * sigma_n(n).
%H Seiichi Manyama, <a href="/A321295/b321295.txt">Table of n, a(n) for n = 1..385</a>
%F G.f.: Sum_{k>=1} k^(k+1)*x^k/(1 - (k*x)^k)^2.
%F a(n) = Sum_{d|n} phi(n/d)*sigma_(n+1)(d).
%F a(n) = n * A023887(n).
%t Table[n DivisorSigma[n, n], {n, 18}]
%t nmax = 18; Rest[CoefficientList[Series[Sum[k^(k + 1) x^k/(1 - (k x)^k)^2, {k, 1, nmax}], {x, 0, nmax}], x]]
%t Table[Sum[EulerPhi[n/d] DivisorSigma[n + 1, d], {d, Divisors[n]}], {n, 18}]
%o (PARI) a(n) = n*sigma(n, n); \\ _Michel Marcus_, Nov 03 2018
%o (Perl) use ntheory ":all"; say "$_ ",vecprod($_,divisor_sum($_,$_)) for 1..30; # _Dana Jacobsen_, Nov 05 2018
%o (Magma) [n*DivisorSigma(n, n): n in [1..20]]; // _Vincenzo Librandi_, Nov 06, 2018
%Y Cf. A023887, A064987.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Nov 02 2018
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