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 A277227 Triangular array T read by rows: T(n,k) gives the additive orders k modulo n, for k = 0,1, ..., n-1. 2
 1, 1, 2, 1, 3, 3, 1, 4, 2, 4, 1, 5, 5, 5, 5, 1, 6, 3, 2, 3, 6, 1, 7, 7, 7, 7, 7, 7, 1, 8, 4, 8, 2, 8, 4, 8, 1, 9, 9, 3, 9, 9, 3, 9, 9, 1, 10, 5, 10, 5, 2, 5, 10, 5, 10, 1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 1, 12, 6, 4, 3, 12, 2, 12, 3, 4, 6, 12 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS As a sequence A054531(n) = a(n+1), n >= 1. As a triangular array this is the row reversed version of A054531. The additive order of an element x of a group (G, +) is the least positive integer j with j*x := x + x + ... + x (j summands) = 0. LINKS Indranil Ghosh, Rows 1..100 of triangle, flattened FORMULA T(n, k) = order of the elements k  of the finite abelian group (Z/(n Z), +), for k = 0, 1, ..., n-1. T(n, k) = n/GCD(n, k), n >= 1, k = 0, 1, ..., n-1. T(n, k) = A054531(n, n-k), n >=1, k = 0, 1, ..., n-1. EXAMPLE The triangle begins: n\k 0  1  2  3  4  5  6  7  8  9 10 11 ... 1:  1 2:  1  2 3:  1  3  3 4:  1  4  2  4 5:  1  5  5  5  5 6:  1  6  3  2  3  6 7:  1  7  7  7  7  7  7 8:  1  8  4  8  2  8  4  8 9:  1  9  9  3  9  9  3  9  9 10: 1 10  5 10  5  2  5 10  5 10 11: 1 11 11 11 11 11 11 11 11 11 11 12: 1 12  6  4  3 12  2 12  3  4  6 12 ... T(n, 0) = 1*0 = 0 = 0 (mod n), and n/GCD(n,0) = n/n = 1. T(4, 2) = 2 because 2 + 2 = 4 = 0 (mod 4) and 2 is not 0 (mod 4). T(4, 2) = n/GCD(2, 4) = 4/2 = 2. CROSSREFS Cf. A054531. Sequence in context: A049834 A134625 A325477 * A054531 A324602 A319226 Adjacent sequences:  A277224 A277225 A277226 * A277228 A277229 A277230 KEYWORD nonn,tabl,easy AUTHOR Wolfdieter Lang, Oct 20 2016 STATUS approved

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Last modified April 12 19:50 EDT 2021. Contains 342932 sequences. (Running on oeis4.)