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%I #16 Oct 29 2022 16:07:22
%S 1,7,28,95,286,802,2143,5519,13807,33762,81060,191678,447396,1032647,
%T 2360593,5351231,12041764,26920297,59829006,132262550,290990077,
%U 637429514,1390811841,3023647046,6551547161,14151910442,30481920523,65480947739,140318385088,299995596747
%N a(n) = Sum_{k=1..n} binomial(n,k) * sigma_2(k).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DivisorFunction.html">Divisor Function</a>.
%F a(n) ~ zeta(3) * n^2 * 2^(n-2).
%F a(n) = Sum_{i=1..n} Sum_{j=1..n} (i^2)*binomial(n,i*j). - _Ridouane Oudra_, Oct 25 2022
%p with(numtheory): seq(add(sigma[2](i)*binomial(n,i),i=1..n), n=1..60); # _Ridouane Oudra_, Oct 25 2022
%t Table[Sum[Binomial[n, k] * DivisorSigma[2, k], {k, 1, n}], {n, 1, 40}]
%o (PARI) a(n) = sum(k=1, n, binomial(n,k) * sigma(k, 2)); \\ _Michel Marcus_, Jul 24 2022
%Y Cf. A001157, A160399, A185003, A356039.
%Y Cf. A006218, A024916, A064602, A064603.
%K nonn
%O 1,2
%A _Vaclav Kotesovec_, Jul 24 2022
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