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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 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 May 17 21:11 EDT 2021. Contains 343990 sequences. (Running on oeis4.)