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).

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, 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, 25, 40, 58, 64, 71, 64, 58, 40, 25, 0, 0, 30, 50, 72, 84, 94, 94, 84, 72, 50, 30, 0

Offset

1,8

Links

Table of n, a(n) for n=1..78.

Example

The array begins:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36, ...
0, 2, 4, 8, 12, 18, 24, 32, 40, 50, 60, 72, ...
0, 4, 8, 15, 22, 33, 44, 58, 72, 90, 108, 129, ...
0, 6, 12, 22, 32, 48, 64, 84, 104, 130, 156, 186, ...
0, 9, 18, 33, 48, 71, 94, 123, 152, 190, 228, 271, ...
0, 12, 24, 44, 64, 94, 124, 162, 200, 250, 300, 356, ...
0, 16, 32, 58, 84, 123, 162, 211, 260, 325, 390, 462, ...
0, 20, 40, 72, 104, 152, 200, 260, 320, 400, 480, 568, ...
0, 25, 50, 90, 130, 190, 250, 325, 400, 499, 598, 707, ...
0, 30, 60, 108, 156, 228, 300, 390, 480, 598, 716, 846, ...
0, 36, 72, 129, 186, 271, 356, 462, 568, 707, 846, 999, ...
...
The initial antidiagonals are:
[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, 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, 25, 40, 58, 64, 71, 64, 58, 40, 25, 0]
[0, 30, 50, 72, 84, 94, 94, 84, 72, 50, 30, 0]
...

Crossrefs

A331762 is the same array displayed as a triangle.

Sequence in context: A134315 A268584 A119332 * A089262 A325788 A240509

Adjacent sequences: A335680 A335681 A335682 * A335684 A335685 A335686

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jul 02 2020

Status

approved