A248470 Put a [+] b = A(A(a) + A(b)), where A = A007913; a(n) is the [+]-sum of binomial(n,i), i=0,...,n.
1, 2, 1, 2, 1, 2, 3, 2, 1, 1, 6, 38, 167, 2095, 1, 2030, 3, 15, 21, 138, 263, 2, 57, 1266, 3470, 7, 145742, 10, 4682335, 110, 38, 618, 366, 83, 3343, 3279, 206555, 215547, 489378, 52010, 21, 5127, 11, 54663, 6203, 5041187, 194, 63038411, 407039, 7602, 2, 2474
Offset: 0
Keywords
Examples
For n=4, we have binomials: 1,4,6,4,1. 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.
Programs
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Mathematica
a7913[n_]:=a7913[n]=Times@@(#[[1]]^Mod[#[[2]],2])&[Transpose[FactorInteger[n]]]; ab[x_,y_]:=ab[x,y]=a7913[a7913[x]+a7913[y]]; Table[Fold[ab,First[#],Rest[#]]&[Binomial[n,#]&[Range[0,n]]],{n,0,50}] (* Peter J. C. Moses, Oct 27 2014 *) -
PARI
a(n) = {s = 0; for (i=0, n, s = core(core(binomial(n, i)) + core(s))); s;} \\ Michel Marcus, Nov 14 2014
Extensions
More terms from Peter J. C. Moses, Oct 27 2014
Comments