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%I #19 Feb 09 2016 06:23:41
%S 1,1,2,1,2,3,1,2,3,4,1,2,3,4,5,1,2,3,5,6,1,2,3,4,5,6,7,1,2,3,4,5,7,8,
%T 1,2,3,4,5,7,8,9,1,2,3,5,7,9,10,1,2,3,4,5,6,7,8,9,10,11,1,2,3,4,5,6,7,
%U 11,12,1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,3,5,7,9,11,13,14
%N Irregular array read by rows: n-th row contains (in numerical order) both the positive integers <= n that are divisors of n and those that are coprime to n.
%C Row n contains A073757(n) terms.
%C The number 1 would appear twice for each n >= 1 if one takes the union of the divisor list of n and the list of the smallest positive reduced residue system modulo n. - _Wolfdieter Lang_, Jan 16 2016
%H Robert Israel, <a href="/A133994/b133994.txt">Table of n, a(n) for n = 1..10003</a> (rows 1 to 174, flattened)
%e The divisors of 12 are: 1,2,3,4,6,12. The positive integers which are <= 12 and are coprime to 12 are: 1,5,7,11. So row 12 is the union of these two sets: 1,2,3,4,5,6,7,11,12.
%e The irregular triangle T(n, k) starts:
%e n\k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
%e 1: 1
%e 2: 1 2
%e 3: 1 2 3
%e 4: 1 2 3 4
%e 5: 1 2 3 4 5
%e 6: 1 2 3 5 6
%e 7: 1 2 3 4 5 6 7
%e 8: 1 2 3 4 5 7 8
%e 9: 1 2 3 4 5 7 8 9
%e 10: 1 2 3 5 7 9 10
%e 11: 1 2 3 4 5 6 7 8 9 10 11
%e 12: 1 2 3 4 5 6 7 11 12
%e 13: 1 2 3 4 5 6 7 8 9 10 11 12 13
%e 14: 1 2 3 5 7 9 11 13 14
%e 15: 1 2 3 4 5 7 8 11 13 14 15
%e 16: 1 2 3 4 5 7 8 9 11 13 15 16
%e 17: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
%e 18: 1 2 3 5 6 7 9 11 13 17 18 19
%e ... Formatted by _Wolfdieter Lang_, Jan 16 2016
%p row:= n -> op(select(t -> member(igcd(t,n), [1,t]), [$1..n])):
%p seq(row(n), n=1..30); # _Robert Israel_, Jan 18 2016
%t row[n_] := Divisors[n] ~Union~ Select[Range[n], CoprimeQ[n, #]&]; Array[ row, 15] // Flatten (* _Jean-François Alcover_, Jan 18 2016 *)
%Y Cf. A073757, A133995.
%K nonn,tabf
%O 1,3
%A _Leroy Quet_, Oct 01 2007
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