A126572 Array read by antidiagonals: a(n,m) = the m-th integer from among those positive integers coprime to n.

1, 1, 2, 1, 3, 3, 1, 2, 5, 4, 1, 3, 4, 7, 5, 1, 2, 5, 5, 9, 6, 1, 5, 3, 7, 7, 11, 7, 1, 2, 7, 4, 9, 8, 13, 8, 1, 3, 3, 11, 6, 11, 10, 15, 9, 1, 2, 5, 4, 13, 7, 13, 11, 17, 10, 1, 3, 4, 7, 5, 17, 8, 15, 13, 19, 11, 1, 2, 7, 5, 9, 6, 19, 9, 17, 14, 21, 12, 1, 5, 3, 9, 7, 11, 8, 23, 11, 19, 16, 23, 13

Offset: 1

Author

Leroy Quet, Dec 28 2006

Keywords

• nonn
• tabl

Comments

From Rémy Sigrist, May 21 2017: (Start)

The n-th row only depends on the radical of n: a(n, m) = a(rad(n), m), where rad(n) = A007947(n).

The n-th row is linear: a(n, m + phi(rad(n))) = a(n, m) + rad(n), where phi(n) = A000010(n) and rad(n) = A007947(n).

(End)

Examples

			Array begins:
1,2,3,4,5,6,7,...
1,3,5,7,9,11,13,...
1,2,4,5,7,8,10,...
1,3,5,7,9,11,13,...
1,2,3,4,6,7,8,...
1,5,7,11,13,17,19,...
1,2,3,4,5,6,8,...
...
		

Crossrefs

Cf. A000010, A007947, A126571, A077581.

Programs

Mathematica

f[m_, n_] := Block[{k = 0, c = n},While[c > 0,k++;While[GCD[k, m] > 1, k++ ];c--;];k];Flatten@Table[f[d - m + 1, m], {d, 13}, {m, d}] (* Ray Chandler, Dec 29 2006 *)

Extensions

Extended by Ray Chandler, Dec 29 2006