Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #13 Aug 17 2019 15:43:17
%S 1,0,0,1,-1,0,2,0,-3,4,0,0,1,0,0,6,-7,0,8,0,-6,8,0,0,-1,0,0,13,-8,0,
%T 12,0,-15,12,0,0,7,0,0,14,-18,0,16,0,-12,24,0,0,-5,0,0,18,-14,0,26,0,
%U -24,20,0,0,6,0,0,32,-31,0,24,0,-18,24,0,0,5,0,0,31,-20,0,28
%N a(0)=1; thereafter a(n) =s(n,3)-s(n,4)-s(n,6)+s(n,12), where s(n,k) = sigma(n/k) if k divides n, otherwise 0.
%H Amiram Eldar, <a href="/A224226/b224226.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.
%p s := proc(n,k)
%p if modp(n,k) = 0 then
%p numtheory[sigma](n/k) ;
%p else
%p 0 ;
%p end if;
%p end proc:
%p A224226 := proc(n)
%p if n = 0 then
%p 1;
%p else
%p s(n,3)-s(n,4)-s(n,6)+s(n,12) ;
%p end if;
%p end proc: # _R. J. Mathar_, Nov 14 2018
%t s[n_, k_] := If[Divisible[n, k], DivisorSigma[1, n/k], 0]; a[0] = 1; a[n_] := s[n, 3] - s[n, 4] - s[n, 6] + 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, s(n,3)-s(n,4)-s(n,6)+s(n,12)); \\ _Michel Marcus_, Sep 27 2017
%Y Cf. A000203, A321527.
%K sign
%O 0,7
%A _N. J. A. Sloane_, Apr 09 2013