

A126572


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


9



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
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OFFSET

1,3


COMMENTS

From Rémy Sigrist, May 21 2017: (Start)
The nth row only depends on the radical of n: a(n, m) = a(rad(n), m), where rad(n) = A007947(n).
The nth 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: A140815 A134840 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



