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%I #8 Oct 15 2013 22:30:16
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,16,32,0,0,0,64,48,0,0,96,0,0,0,
%T 192,256,0,256,384,0,0,0,0,0,832,768,512,0,0,0,0,384,576,1536,3072,
%U 2048,8448,7680,5632,0,0,0,14336,3584,0,0,3072
%N Max_{k=0..n} d(C(n,k)) - d(C(n,[ n/2 ])), where d() = number of divisors.
%e n=20, d(C[ 20,10 ])= 48 and the d(C[ 20,k ]) values are 1,6,8,16,24,40,64,80. The maximum is 80, so the difference is 80-48 = 32.
%t Table[Max[Table[DivisorSigma[0,Binomial[n,k]],{k,0,n}]] - DivisorSigma[ 0,Binomial[n,Floor[n/2]]],{n,70}] (* _Harvey P. Dale_, Jul 18 2013 *)
%Y Cf. A000005, A048485, A048569.
%K nonn
%O 1,18
%A _Labos Elemer_
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