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

1,3

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)

Links

Table of n, a(n) for n=1..91.

Example

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,...
...

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 *)

Crossrefs

Cf. A000010, A007947, A126571, A077581.

Sequence in context: A134840 A352356 A229742 * A162910 A098975 A309213

Adjacent sequences: A126569 A126570 A126571 * A126573 A126574 A126575

Keyword

nonn,tabl

Author

Leroy Quet, Dec 28 2006

Extensions

Extended by Ray Chandler, Dec 29 2006

Status

approved