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A216627 Triangle read by rows, n>=1, 1<=k<=n, T(n,k) = sum_{c|n,d|k} lcm(c,d).

%I A216627 #14 Oct 09 2016 08:49:04
%S A216627 1,3,7,4,12,10,7,15,28,27,6,18,24,42,16,12,28,30,60,72,70,8,24,32,56,
%T A216627 48,96,22,15,31,60,51,90,124,120,83,13,39,28,91,78,84,104,195,55,18,
%U A216627 42,72,90,48,168,144,186,234,112,12,36,48,84,72,144,96,180,156
%N A216627 Triangle read by rows, n>=1, 1<=k<=n, T(n,k) = sum_{c|n,d|k} lcm(c,d).
%C A216627 This is the lower triangular array of A216626, which is the main entry for this sequence.
%H A216627 Alois P. Heinz, <a href="/A216627/b216627.txt">Rows n = 1..141, flattened</a>
%F A216627 T(n,1) = A000203(n) = sigma(n).
%F A216627 T(n,n) = A064950(n) = sum_{d|n} d*tau(d^2).
%e A216627 The first rows of the triangle are:
%e A216627 1;
%e A216627 3,   7;
%e A216627 4,  12, 10;
%e A216627 7,  15, 28, 27;
%e A216627 6,  18, 24, 42, 16;
%e A216627 12, 28, 30, 60, 72,  70;
%e A216627 8,  24, 32, 56, 48,  96,  22;
%e A216627 15, 31, 60, 51, 90, 124, 120,  83;
%e A216627 13, 39, 28, 91, 78,  84, 104, 195, 55;
%p A216627 with(numtheory):
%p A216627 T:= (n, k) -> add(add(ilcm(c, d), c=divisors(n)), d=divisors(k));
%p A216627 seq (seq (T(n, k), k=1..n), n=1..12);  # _Alois P. Heinz_, Sep 12 2012
%t A216627 T[n_, k_] := Sum[LCM[c, d], {c, Divisors[n]}, {d, Divisors[k]}]; Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Mar 25 2014 *)
%o A216627 (Sage)
%o A216627 for n in (1..9): [A216626(n,k) for k in (1..n)]
%Y A216627 Cf. A216620, A216621, A216622, A216623, A216624, A216625, A216626.
%K A216627 nonn,tabl
%O A216627 1,2
%A A216627 _Peter Luschny_, Sep 12 2012