A020740 Max_{k=0..n} d(C(n,k)) - d(C(n,[ n/2 ])), where d() = number of divisors.

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, 192, 256, 0, 256, 384, 0, 0, 0, 0, 0, 832, 768, 512, 0, 0, 0, 0, 384, 576, 1536, 3072, 2048, 8448, 7680, 5632, 0, 0, 0, 14336, 3584, 0, 0, 3072

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A000005, A048485, A048569.

Programs

Maple

020740 := proc(n)
    local a,k;
    a := -1 ;
    for k from 0 to n do
        a := max(a, numtheory[tau](binomial(n,k))) ;
    end do:
    a-numtheory[tau](binomial(n,floor(n/2))) ;
end proc:
seq(A020740(n),n=1..80); # R. J. Mathar, Nov 19 2024

Mathematica

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 *)