A333292 Triangle read by rows: T(m,n) = Sum_{ 1 <= i <= m, 1 <= j <= n, gcd(i,j)=1 } i*j, for 1 <= n <= m.

1, 3, 5, 6, 14, 23, 10, 18, 39, 55, 15, 33, 69, 105, 155, 21, 39, 75, 111, 191, 227, 28, 60, 117, 181, 296, 374, 521, 36, 68, 149, 213, 368, 446, 649, 777, 45, 95, 176, 276, 476, 554, 820, 1020, 1263, 55, 105, 216, 316, 516, 594, 930, 1130, 1463, 1663, 66, 138, 282, 426, 681, 825, 1238, 1526, 1958, 2268, 2873

Offset: 1

Author

N. J. A. Sloane, Mar 23 2020

Keywords

• nonn
• tabl

Comments

The last two diagonals are A333293, Sum_{k=1..n-1} k^2*phi(k) + n^2*phi(n)/2, and A319087, Sum_{k=1..n} k^2*phi(k), where phi = A000010. Is there a similar formula for the general term?

Examples

			Triangle begins:
1,
3, 5,
6, 14, 23,
10, 18, 39, 55,
15, 33, 69, 105, 155,
21, 39, 75, 111, 191, 227,
28, 60, 117, 181, 296, 374, 521,
36, 68, 149, 213, 368, 446, 649, 777,
45, 95, 176, 276, 476, 554, 820, 1020, 1263,
55, 105, 216, 316, 516, 594, 930, 1130, 1463, 1663,
...
		

Links

• Alois P. Heinz, Rows n = 1..141, flattened

Crossrefs

First two columns are A000217 and A074378, rightmost two diagonals are A333293 and A319087.

Main diagonal is A319087.

Cf. A320541.

Programs

Maple

T:= (m, n)-> add(add(`if`(igcd(i, j)=1, i*j, 0), j=1..n), i=1..m):
seq(seq(T(m, n), n=1..m), m=1..12);  # Alois P. Heinz, Mar 23 2020