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A133994
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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.
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2
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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, 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, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1, 2, 3, 5, 7, 9, 11, 13, 14
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OFFSET
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1,3
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COMMENTS
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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
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LINKS
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EXAMPLE
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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.
The irregular triangle T(n, k) starts:
n\k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
1: 1
2: 1 2
3: 1 2 3
4: 1 2 3 4
5: 1 2 3 4 5
6: 1 2 3 5 6
7: 1 2 3 4 5 6 7
8: 1 2 3 4 5 7 8
9: 1 2 3 4 5 7 8 9
10: 1 2 3 5 7 9 10
11: 1 2 3 4 5 6 7 8 9 10 11
12: 1 2 3 4 5 6 7 11 12
13: 1 2 3 4 5 6 7 8 9 10 11 12 13
14: 1 2 3 5 7 9 11 13 14
15: 1 2 3 4 5 7 8 11 13 14 15
16: 1 2 3 4 5 7 8 9 11 13 15 16
17: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18: 1 2 3 5 6 7 9 11 13 17 18 19
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MAPLE
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row:= n -> op(select(t -> member(igcd(t, n), [1, t]), [$1..n])):
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MATHEMATICA
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row[n_] := Divisors[n] ~Union~ Select[Range[n], CoprimeQ[n, #]&]; Array[ row, 15] // Flatten (* Jean-François Alcover, Jan 18 2016 *)
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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