cp's OEIS Frontend

A335683 Array read by antidiagonals: T(n,k) (n >= 1, k >= 1) = Sum_{i=1..n, j=1..k, gcd(i,j)=2} (n+1-i)*(k+1-j).

%I A335683 #11 Jan 04 2024 21:12:13
%S A335683 0,0,0,0,1,0,0,2,2,0,0,4,4,4,0,0,6,8,8,6,0,0,9,12,15,12,9,0,0,12,18,
%T A335683 22,22,18,12,0,0,16,24,33,32,33,24,16,0,0,20,32,44,48,48,44,32,20,0,0,
%U A335683 25,40,58,64,71,64,58,40,25,0,0,30,50,72,84,94,94,84,72,50,30,0
%N A335683 Array read by antidiagonals: T(n,k) (n >= 1, k >= 1) = Sum_{i=1..n, j=1..k, gcd(i,j)=2} (n+1-i)*(k+1-j).
%e A335683 The array begins:
%e A335683 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e A335683 0, 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36, ...
%e A335683 0, 2, 4, 8, 12, 18, 24, 32, 40, 50, 60, 72, ...
%e A335683 0, 4, 8, 15, 22, 33, 44, 58, 72, 90, 108, 129, ...
%e A335683 0, 6, 12, 22, 32, 48, 64, 84, 104, 130, 156, 186, ...
%e A335683 0, 9, 18, 33, 48, 71, 94, 123, 152, 190, 228, 271, ...
%e A335683 0, 12, 24, 44, 64, 94, 124, 162, 200, 250, 300, 356, ...
%e A335683 0, 16, 32, 58, 84, 123, 162, 211, 260, 325, 390, 462, ...
%e A335683 0, 20, 40, 72, 104, 152, 200, 260, 320, 400, 480, 568, ...
%e A335683 0, 25, 50, 90, 130, 190, 250, 325, 400, 499, 598, 707, ...
%e A335683 0, 30, 60, 108, 156, 228, 300, 390, 480, 598, 716, 846, ...
%e A335683 0, 36, 72, 129, 186, 271, 356, 462, 568, 707, 846, 999, ...
%e A335683 ...
%e A335683 The initial antidiagonals are:
%e A335683 [0]
%e A335683 [0, 0]
%e A335683 [0, 1, 0]
%e A335683 [0, 2, 2, 0]
%e A335683 [0, 4, 4, 4, 0]
%e A335683 [0, 6, 8, 8, 6, 0]
%e A335683 [0, 9, 12, 15, 12, 9, 0]
%e A335683 [0, 12, 18, 22, 22, 18, 12, 0]
%e A335683 [0, 16, 24, 33, 32, 33, 24, 16, 0]
%e A335683 [0, 20, 32, 44, 48, 48, 44, 32, 20, 0]
%e A335683 [0, 25, 40, 58, 64, 71, 64, 58, 40, 25, 0]
%e A335683 [0, 30, 50, 72, 84, 94, 94, 84, 72, 50, 30, 0]
%e A335683 ...
%Y A335683 A331762 is the same array displayed as a triangle.
%K A335683 nonn,tabl
%O A335683 1,8
%A A335683 _N. J. A. Sloane_, Jul 02 2020