A020740 - OEIS

%I #10 Nov 19 2024 08:51:29

%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.

%p 020740 := proc(n)

%p     local a,k;

%p     a := -1 ;

%p     for k from 0 to n do

%p         a := max(a, numtheory[tau](binomial(n,k))) ;

%p     end do:

%p     a-numtheory[tau](binomial(n,floor(n/2))) ;

%p end proc:

%p seq(A020740(n),n=1..80); # _R. J. Mathar_, Nov 19 2024

%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_