A308477 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals: A(n,k) = Sum_{j=1..n, gcd(n,j) = 1} j^k.

1, 1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 5, 4, 4, 1, 1, 9, 10, 10, 2, 1, 1, 17, 28, 30, 6, 6, 1, 1, 33, 82, 100, 26, 21, 4, 1, 1, 65, 244, 354, 126, 91, 16, 6, 1, 1, 129, 730, 1300, 626, 441, 84, 27, 4, 1, 1, 257, 2188, 4890, 3126, 2275, 496, 159, 20, 10, 1, 1, 513, 6562, 18700, 15626, 12201, 3108, 1053, 140, 55, 4

Offset: 1

Author

Ilya Gutkovskiy, May 29 2019

Keywords

• nonn
• tabl

Examples

			Square array begins:
  1,   1,   1,    1,    1,     1,  ...
  1,   1,   1,    1,    1,     1,  ...
  2,   3,   5,    9,   17,    33,  ...
  2,   4,  10,   28,   82,   244,  ...
  4,  10,  30,  100,  354,  1300,  ...
  2,   6,  26,  126,  626,  3126,  ...
		

Links

• Seiichi Manyama, Antidiagonals n = 1..140, flattened

Crossrefs

Columns k=0..4 give A000010, A023896, A053818, A053819, A053820.

Cf. A103438.

Programs

Mathematica

Table[Function[k, Sum[If[GCD[n, j] == 1, j^k, 0], {j, 1, n}]][i - n], {i, 0, 12}, {n, 1, i}] // Flatten