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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-Fran├žois Alcover, Jan 18 2016 *)

CROSSREFS

Cf. A073757, A133995.

Sequence in context: A243732 A194905 A243730 * A066041 A194965 A243712

Adjacent sequences:  A133991 A133992 A133993 * A133995 A133996 A133997

KEYWORD

nonn,tabf

AUTHOR

Leroy Quet, Oct 01 2007

STATUS

approved

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Last modified April 12 10:52 EDT 2021. Contains 342920 sequences. (Running on oeis4.)