A102716 Triangle read by rows: T(n,k) = sigma(binomial(n,k)) (0 <= k <= n), where sigma(m) is the sum of the positive divisors of m.

1, 1, 1, 1, 3, 1, 1, 4, 4, 1, 1, 7, 12, 7, 1, 1, 6, 18, 18, 6, 1, 1, 12, 24, 42, 24, 12, 1, 1, 8, 32, 48, 48, 32, 8, 1, 1, 15, 56, 120, 144, 120, 56, 15, 1, 1, 13, 91, 224, 312, 312, 224, 91, 13, 1, 1, 18, 78, 360, 576, 728, 576, 360, 78, 18, 1, 1, 12, 72, 288, 864, 1152, 1152, 864

Offset: 0

Author

Emeric Deutsch, Feb 06 2005

Keywords

• nonn
• tabl

Comments

Row n contains n+1 terms. Row sums yield A074801. T(2n,n) = A067819(n).

Examples

			T(6,3)=42 because the sum of the divisors of binomial(6,3)=20 is 1+2+4+5+10+20=42.
Triangle begins:
  1;
  1,  1;
  1,  3,  1;
  1,  4,  4,  1;
  1,  7, 12,  7,  1;
		

Links

• T. D. Noe, Rows n = 0..100 of triangle, flattened

Crossrefs

Cf. A074801, A067819.

Programs

Maple

with(numtheory): T:=(n,k)->sigma(binomial(n,k)): for n from 0 to 11 do seq(T(n,k),k=0..n) od; # yields sequence in triangular form

Mathematica

Table[DivisorSigma[1,Binomial[n,k]],{n,0,20},{k,0,n}]//Flatten (* Harvey P. Dale, Mar 25 2016 *)

Formula

T(n, k) = sigma(binomial(n, k)) (0 <= k <= n).