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

%I A126572 #14 Oct 10 2019 13:48:15
%S A126572 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,
%T A126572 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,
%U A126572 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
%N A126572 Array read by antidiagonals: a(n,m) = the m-th integer from among those positive integers coprime to n.
%C A126572 From _Rémy Sigrist_, May 21 2017: (Start)
%C A126572 The n-th row only depends on the radical of n: a(n, m) = a(rad(n), m), where rad(n) = A007947(n).
%C A126572 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).
%C A126572 (End)
%e A126572 Array begins:
%e A126572 1,2,3,4,5,6,7,...
%e A126572 1,3,5,7,9,11,13,...
%e A126572 1,2,4,5,7,8,10,...
%e A126572 1,3,5,7,9,11,13,...
%e A126572 1,2,3,4,6,7,8,...
%e A126572 1,5,7,11,13,17,19,...
%e A126572 1,2,3,4,5,6,8,...
%e A126572 ...
%t A126572 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 *)
%Y A126572 Cf. A000010, A007947, A126571, A077581.
%K A126572 nonn,tabl
%O A126572 1,3
%A A126572 _Leroy Quet_, Dec 28 2006
%E A126572 Extended by _Ray Chandler_, Dec 29 2006