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A133994 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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Row n contains A073757(n) terms.
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
LINKS
Robert Israel, Table of n, a(n) for n = 1..10003 (rows 1 to 174, flattened)
EXAMPLE
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
... Formatted by Wolfdieter Lang, Jan 16 2016
MAPLE
row:= n -> op(select(t -> member(igcd(t, n), [1, t]), [$1..n])):
seq(row(n), n=1..30); # Robert Israel, Jan 18 2016
MATHEMATICA
row[n_] := Divisors[n] ~Union~ Select[Range[n], CoprimeQ[n, #]&]; Array[ row, 15] // Flatten (* Jean-François Alcover, Jan 18 2016 *)
CROSSREFS
Sequence in context: A243732 A194905 A243730 * A066041 A194965 A243712
KEYWORD
nonn,tabf
AUTHOR
Leroy Quet, Oct 01 2007
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)