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%I #31 Nov 14 2014 13:06:30
%S 1,2,1,2,1,2,3,2,1,1,6,38,167,2095,1,2030,3,15,21,138,263,2,57,1266,
%T 3470,7,145742,10,4682335,110,38,618,366,83,3343,3279,206555,215547,
%U 489378,52010,21,5127,11,54663,6203,5041187,194,63038411,407039,7602,2,2474
%N Put a [+] b = A(A(a) + A(b)), where A = A007913; a(n) is the [+]-sum of binomial(n,i), i=0,...,n.
%C By definition, all terms are squarefree (A005117).
%e For n=4, we have binomials: 1,4,6,4,1.
%e To obtain a(4), we form the sums 1[+]4 = 1[+]1 = 2; 2[+]6 = 2; 2[+]4 = 2[+]1 = 3; 3[+]1=1. So a(4)=1.
%t a7913[n_]:=a7913[n]=Times@@(#[[1]]^Mod[#[[2]],2])&[Transpose[FactorInteger[n]]];
%t ab[x_,y_]:=ab[x,y]=a7913[a7913[x]+a7913[y]];
%t Table[Fold[ab,First[#],Rest[#]]&[Binomial[n,#]&[Range[0,n]]],{n,0,50}] (* _Peter J. C. Moses_, Oct 27 2014 *)
%o (PARI) a(n) = {s = 0; for (i=0, n, s = core(core(binomial(n, i)) + core(s))); s;} \\ _Michel Marcus_, Nov 14 2014
%Y Cf. A005117, A007318, A007913.
%K nonn
%O 0,2
%A _Vladimir Shevelev_, Oct 27 2014
%E More terms from _Peter J. C. Moses_, Oct 27 2014
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