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

1,18

Links

Table of n, a(n) for n=1..64.

Example

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.

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 *)

Crossrefs

Cf. A000005, A048485, A048569.

Sequence in context: A334560 A357631 A109240 * A344021 A086980 A256934

Adjacent sequences: A020737 A020738 A020739 * A020741 A020742 A020743

Keyword

nonn,changed

Author

Labos Elemer

Status

approved