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

0,5

Comments

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

Links

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

Formula

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

Example

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;

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 *)

Crossrefs

Cf. A074801, A067819.

Sequence in context: A026374 A174032 A180979 * A173076 A134510 A335322

Adjacent sequences: A102713 A102714 A102715 * A102717 A102718 A102719

Keyword

nonn,tabl

Author

Emeric Deutsch, Feb 06 2005

Status

approved