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 A054521 Triangle T(n,k): T(n,k) = 1 if gcd(n, k) = 1, T(n,k) = 0 otherwise (n >= 1, 1 <= k <= n). 54
 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row sums = phi(n), A000010: (1, 1, 2, 2, 4, 2, 6, ...). - Gary W. Adamson, May 20 2007 Characteristic function of A169581: a(A169581(n)) = 1; a(A169582(n)) = 0. - Reinhard Zumkeller, Dec 02 2009 The function T(n,k) = T(k,n) is defined for k > n but only the values for 1 <= k <= n as a triangular array are listed here. T(n,k) = |K(n-k|k)| where K(i|j) is the Kronecker symbol. - Peter Luschny, Aug 05 2012 Twice the sum over the antidiagonals, starting with entry T(n-1,1), for n >= 3, is the same as the row n sum (i.e., phi(n): 2*Sum_{k=1..floor(n/2)} T(n-k,k) = phi(n), n >= 3). - Wolfdieter Lang, Apr 26 2013 The number of zeros in the n-th row of the triangle is cototient(n) = A051953(n). - Omar E. Pol, Apr 21 2017 LINKS Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened Jakub Jaroslaw Ciaston, A054531 vs A164306 (plot shows these ones) FORMULA T(n,k) = A063524(A050873(n,k)). - Reinhard Zumkeller, Dec 02 2009, corrected Sep 03 2015 T(n,k) = A054431(n,k) = A054431(k,n). - R. J. Mathar, Jul 21 2016 EXAMPLE The triangle T(n,k) begins: n\k  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 ... 1:   1 2:   1  0 3:   1  1  0 4:   1  0  1  0 5:   1  1  1  1  0 6:   1  0  0  0  1  0 7:   1  1  1  1  1  1  0 8:   1  0  1  0  1  0  1  0 9:   1  1  0  1  1  0  1  1  0 10:  1  0  1  0  0  0  1  0  1  0 11:  1  1  1  1  1  1  1  1  1  1  0 12:  1  0  0  0  1  0  1  0  0  0  1  0 13:  1  1  1  1  1  1  1  1  1  1  1  1  0 14:  1  0  1  0  1  0  0  0  1  0  1  0  1  0 15:  1  1  0  1  0  0  1  1  0  0  1  0  1  1  0 ... (Reformatted by Wolfdieter Lang, Apr 26 2013) Sums over antidiagonals: n = 3: 2*T(2,1) = 2 = T(3,1) + T(3,2) = phi(3). n = 4: 2*(T(3,1) + T(2,2)) = 2 = phi(4), etc. - Wolfdieter Lang, Apr 26 2013 MAPLE A054521_row := n -> seq(abs(numtheory[jacobi](n-k, k)), k=1..n); for n from 1 to 13 do A054521_row(n) od; # Peter Luschny, Aug 05 2012 MATHEMATICA T[ n_, k_] := Boole[ n>0 && k>0 && GCD[ n, k] == 1] (* Michael Somos, Jul 17 2011 *) T[ n_, k_] := If[ n<1 || k<1, 0, If[ k>n, T[ k, n], If[ k==1, 1, If[ n>k, T[ k, Mod[ n, k, 1]], 0]]] (* Michael Somos, Jul 17 2011 *) PROG (PARI) {T(n, k) = n>0 && k>0 && gcd(n, k)==1} /* Michael Somos, Jul 17 2011 */ (Sage) def A054521_row(n): return [abs(kronecker_symbol(n-k, k)) for k in (1..n)] for n in (1..13): print(A054521_row(n)) # Peter Luschny, Aug 05 2012 (Haskell) a054521 n k = a054521_tabl !! (n-1) !! (k-1) a054521_row n = a054521_tabl !! (n-1) a054521_tabl = map (map a063524) a050873_tabl a054521_list = concat a054521_tabl -- Reinhard Zumkeller, Sep 03 2015 CROSSREFS Cf. A051731, A054522, A215200. Cf. A050873, A063524. Sequence in context: A128431 A290452 A215200 * A338354 A014240 A014471 Adjacent sequences:  A054518 A054519 A054520 * A054522 A054523 A054524 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Apr 09 2000 STATUS approved

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Last modified January 17 00:41 EST 2021. Contains 340213 sequences. (Running on oeis4.)