Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #5 Apr 11 2019 21:25:57
%S 0,1,6,17,36,64,108,172,240,340,444,612,744,980,1164,1504,1704,2172,
%T 2388,2964,3288,3968,4272,5272,5520,6624,7104,8276,8640,10404,10572,
%U 12480,13032,14988,15300,18204,18048,21004,21636,24616,24648,29036,28452,32768,33552,37488
%N Self-convolution of the Dedekind psi function (A001615).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DedekindFunction.html">Dedekind Function</a>
%F G.f.: (Sum_{k>=1} mu(k)^2*x^k/(1 - x^k)^2)^2.
%F a(n) = Sum_{k=1..n-1} A001615(k)*A001615(n-k).
%t Rest[nmax = 46; CoefficientList[Series[Sum[MoebiusMu[k]^2 x^k/(1 - x^k)^2, {k, 1, nmax}]^2, {x, 0, nmax}], x]]
%t psi[n_] := psi[n] = Sum[MoebiusMu[n/d]^2 d, {d, Divisors @ n}]; a[n_] := a[n] = Sum[psi[k] psi[n - k], {k, 1, n - 1}]; Table[a[n], {n, 1, 46}]
%Y Cf. A001615, A008683, A065093, A307309.
%K nonn
%O 1,3
%A _Ilya Gutkovskiy_, Apr 11 2019