A331781 Triangle read by rows: T(m,n) = Sum_{0<i<m, 0<j<n, gcd{i,j}=1} 1, where m >= n >= 1.

0, 0, 1, 0, 2, 3, 0, 3, 5, 7, 0, 4, 6, 9, 11, 0, 5, 8, 12, 15, 19, 0, 6, 9, 13, 16, 21, 23, 0, 7, 11, 16, 20, 26, 29, 35, 0, 8, 12, 18, 22, 29, 32, 39, 43, 0, 9, 14, 20, 25, 33, 36, 44, 49, 55, 0, 10, 15, 22, 27, 35, 38, 47, 52, 59, 63, 0, 11, 17, 25, 31, 40, 44, 54, 60, 68, 73, 83

Offset

1,5

Links

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

M. A. Alekseyev, M. Basova, and N. Yu. Zolotykh. On the minimal teaching sets of two-dimensional threshold functions. SIAM Journal on Discrete Mathematics 29:1 (2015), 157-165. doi:10.1137/140978090. See Lemma 11.

Example

Triangle begins:
0,
0, 1,
0, 2, 3,
0, 3, 5, 7,
0, 4, 6, 9, 11,
0, 5, 8, 12, 15, 19,
0, 6, 9, 13, 16, 21, 23,
0, 7, 11, 16, 20, 26, 29, 35,
0, 8, 12, 18, 22, 29, 32, 39, 43,
0, 9, 14, 20, 25, 33, 36, 44, 49, 55
...

Maple

VS := proc(m, n) local a, i, j; a:=0;
for i from 1 to m-1 do for j from 1 to n-1 do
if gcd(i, j)=1 then a:=a+1; fi; od: od: a; end;
for m from 1 to 12 do lprint([seq(VS(m, n), n=1..m)]); od:

Mathematica

Table[Sum[Boole[# == 1] # &@ GCD[i, j], {i, m - 1}, {j, n - 1}], {m, 12}, {n, m}] // Flatten (* Michael De Vlieger, Feb 12 2020 *)

Crossrefs

Main diagonal is A018805.

A333295 is essentially the same array.

Sequence in context: A227536 A047773 A279416 * A376484 A187988 A035549

Adjacent sequences: A331778 A331779 A331780 * A331782 A331783 A331784

Keyword

nonn,tabl

Author

N. J. A. Sloane, Feb 11 2020

Status

approved