A333295 Triangle read by rows: T(m,n) = Sum_{1 <= i <= m, 1 <= j <= n, gcd{i,j}=1} 1, where m >= n >= 1.

1, 2, 3, 3, 5, 7, 4, 6, 9, 11, 5, 8, 12, 15, 19, 6, 9, 13, 16, 21, 23, 7, 11, 16, 20, 26, 29, 35, 8, 12, 18, 22, 29, 32, 39, 43, 9, 14, 20, 25, 33, 36, 44, 49, 55, 10, 15, 22, 27, 35, 38, 47, 52, 59, 63, 11, 17, 25, 31, 40, 44, 54, 60, 68, 73, 83, 12, 18, 26, 32, 42, 46, 57, 63, 71, 76, 87, 91

Offset: 1

Author

N. J. A. Sloane, Mar 24 2020

Keywords

• nonn
• tabl

Comments

This is the same triangle as A331781, except the initial row and column of 0's is missing.

Examples

			Triangle begins:
1,
2, 3,
3, 5, 7,
4, 6, 9, 11,
5, 8, 12, 15, 19,
6, 9, 13, 16, 21, 23,
7, 11, 16, 20, 26, 29, 35,
8, 12, 18, 22, 29, 32, 39, 43,
9, 14, 20, 25, 33, 36, 44, 49, 55,
10, 15, 22, 27, 35, 38, 47, 52, 59, 63,
11, 17, 25, 31, 40, 44, 54, 60, 68, 73, 83,
12, 18, 26, 32, 42, 46, 57, 63, 71, 76, 87, 91,
...
		

Crossrefs

Cf. A331781. Main diagonal is A018805.

Programs

Maple

V0 := proc(m,n) local a,i,j; a:=0;
for i from 1 to m do for j from 1 to n do
if igcd(i,j)=1 then a:=a+1; fi; od: od: a; end;
for m from 1 to 14 do lprint([seq(V0(m,n),n=1..m)]); od: