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%I #15 Aug 17 2019 15:43:42
%S 1,2,3,8,9,12,21,16,21,26,18,24,27,28,24,48,45,36,75,40,54,64,36,48,
%T 39,62,42,80,72,60,126,64,93,96,54,96,81,76,60,112,126,84,168,88,108,
%U 156,72,96,63,114,93,144,126,108,237,144,168,160,90,120,162,124,96,208,189,168,252,136,162,192,144,144,93,148,114,248,180,192,294,160,270
%N a(0)=1; thereafter a(n) = 2*s(n,1)-3*s(n,2)+4*s(n,4)+9*s(n,6)-36*s(n,12), where s(n,k) = sigma(n/k) if k divides n, otherwise 0.
%H Amiram Eldar, <a href="/A224225/b224225.txt">Table of n, a(n) for n = 0..10000</a>
%H K. S. Williams, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.120.04.329">The parents of Jacobi's four squares theorem are unique</a>, Amer. Math. Monthly, 120 (2013), 329-345.
%t s[n_, k_] := If[Divisible[n, k], DivisorSigma[1, n/k], 0]; a[0] = 1; a[n_] := 2*s[n, 1] - 3*s[n, 2] + 4*s[n, 4] + 9*s[n, 6] - 36*s[ n, 12]; Array[a, 100, 0] (* _Amiram Eldar_, Aug 17 2019 *)
%o (PARI) s(n,k) = if (!(n%k), sigma(n/k), 0);
%o a(n) = if (n==0, 1, 2*s(n,1)-3*s(n,2)+4*s(n,4)+9*s(n,6)-36*s(n,12)); \\ _Michel Marcus_, Sep 27 2017
%Y Cf. A000203.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Apr 09 2013