cp's OEIS Frontend

A216626 Square array read by antidiagonals, T(n,k) = sum_{c|n,d|k} lcm(c,d) for n>=1, k>=1.

%I A216626 #14 Mar 08 2020 00:07:12
%S A216626 1,3,3,4,7,4,7,12,12,7,6,15,10,15,6,12,18,28,28,18,12,8,28,24,27,24,
%T A216626 28,8,15,24,30,42,42,30,24,15,13,31,32,60,16,60,32,31,13,18,39,60,56,
%U A216626 72,72,56,60,39,18,12,42,28,51,48,70,48,51,28,42,12,28,36
%N A216626 Square array read by antidiagonals, T(n,k) = sum_{c|n,d|k} lcm(c,d) for n>=1, k>=1.
%C A216626 T(n,n) = A064950(n) = sum_{d|n} d*tau(d^2).
%C A216626 T(n,1) = T(1,n) = A000203(n) = sigma(n).
%C A216626 T(n,2) = T(2,n) = A062731(n) = sigma(2*n).
%C A216626 T(n+1,n) = A083539(n) = sigma(n+1)*sigma(n).
%C A216626 T(prime(n),1) = A008864(n) = prime(n)+1.
%H A216626 Alois P. Heinz, <a href="/A216626/b216626.txt">Antidiagonals n = 1..141, flattened</a>
%e A216626 [-----1---2---3----4----5----6----7----8----9---10---11---12]
%e A216626 [ 1]  1,  3,  4,   7,   6,  12,   8,  15,  13,  18,  12,  28
%e A216626 [ 2]  3,  7, 12,  15,  18,  28,  24,  31,  39,  42,  36,  60
%e A216626 [ 3]  4, 12, 10,  28,  24,  30,  32,  60,  28,  72,  48,  70
%e A216626 [ 4]  7, 15, 28,  27,  42,  60,  56,  51,  91,  90,  84, 108
%e A216626 [ 5]  6, 18, 24,  42,  16,  72,  48,  90,  78,  48,  72, 168
%e A216626 [ 6] 12, 28, 30,  60,  72,  70,  96, 124,  84, 168, 144, 150
%e A216626 [ 7]  8, 24, 32,  56,  48,  96,  22, 120, 104, 144,  96, 224
%e A216626 [ 8] 15, 31, 60,  51,  90, 124, 120,  83, 195, 186, 180, 204
%e A216626 [ 9] 13, 39, 28,  91,  78,  84, 104, 195,  55, 234, 156, 196
%e A216626 [10] 18, 42, 72,  90,  48, 168, 144, 186, 234, 112, 216, 360
%e A216626 [11] 12, 36, 48,  84,  72, 144,  96, 180, 156, 216,  34, 336
%e A216626 [12] 28, 60, 70, 108, 168, 150, 224, 204, 196, 360, 336, 270
%e A216626 .
%e A216626 Displayed as a triangular array:
%e A216626     1;
%e A216626     3,  3;
%e A216626     4,  7,  4;
%e A216626     7, 12, 12,  7;
%e A216626     6, 15, 10, 15,  6;
%e A216626    12, 18, 28, 28, 18, 12;
%e A216626     8, 28, 24, 27, 24, 28,  8;
%e A216626    15, 24, 30, 42, 42, 30, 24, 15;
%e A216626    13, 31, 32, 60, 16, 60, 32, 31, 13;
%p A216626 with(numtheory):
%p A216626 T:= (n, k) -> add(add(ilcm(c, d), c=divisors(n)), d=divisors(k)):
%p A216626 seq (seq (T(n, 1+d-n), n=1..d), d=1..12);  # _Alois P. Heinz_, Sep 12 2012
%t A216626 T[n_, k_] := Sum[LCM[c, d], {c, Divisors[n]}, {d, Divisors[k]}]; Table[T[n-k+1, k], {n, 1, 12}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Mar 25 2014 *)
%o A216626 (Sage)
%o A216626 def A216626(n, k) :
%o A216626     cp = cartesian_product([divisors(n), divisors(k)])
%o A216626     return reduce(lambda x,y: x+y, map(lcm, cp))
%o A216626 for n in (1..12): [A216626(n,k) for k in (1..12)]
%Y A216626 Cf. A216620, A216621, A216622, A216623, A216624, A216625, A216627.
%K A216626 nonn,tabl
%O A216626 1,2
%A A216626 _Peter Luschny_, Sep 12 2012