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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.

%I A102716 #11 Jul 23 2019 02:02:44
%S A102716 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,
%T A102716 32,48,48,32,8,1,1,15,56,120,144,120,56,15,1,1,13,91,224,312,312,224,
%U A102716 91,13,1,1,18,78,360,576,728,576,360,78,18,1,1,12,72,288,864,1152,1152,864
%N 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.
%C A102716 Row n contains n+1 terms. Row sums yield A074801. T(2n,n) = A067819(n).
%H A102716 T. D. Noe, <a href="/A102716/b102716.txt">Rows n = 0..100 of triangle, flattened</a>
%F A102716 T(n, k) = sigma(binomial(n, k)) (0 <= k <= n).
%e A102716 T(6,3)=42 because the sum of the divisors of binomial(6,3)=20 is 1+2+4+5+10+20=42.
%e A102716 Triangle begins:
%e A102716   1;
%e A102716   1,  1;
%e A102716   1,  3,  1;
%e A102716   1,  4,  4,  1;
%e A102716   1,  7, 12,  7,  1;
%p A102716 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
%t A102716 Table[DivisorSigma[1,Binomial[n,k]],{n,0,20},{k,0,n}]//Flatten (* _Harvey P. Dale_, Mar 25 2016 *)
%Y A102716 Cf. A074801, A067819.
%K A102716 nonn,tabl
%O A102716 0,5
%A A102716 _Emeric Deutsch_, Feb 06 2005