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 A048158 Triangular array T read by rows: T(n,k) = n mod k, for k=1,2,...,n, n=1,2,... 16
 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 1, 3, 2, 1, 0, 0, 0, 2, 0, 3, 2, 1, 0, 0, 1, 0, 1, 4, 3, 2, 1, 0, 0, 0, 1, 2, 0, 4, 3, 2, 1, 0, 0, 1, 2, 3, 1, 5, 4, 3, 2, 1, 0, 0, 0, 0, 0, 2, 0, 5, 4, 3, 2, 1, 0, 0, 1, 1, 1, 3, 1, 6, 5, 4, 3, 2, 1, 0, 0, 0, 2, 2, 4, 2, 0, 6, 5, 4, 3, 2, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,13 COMMENTS Also, rectangular array read by antidiagonals: a(n, k) = n%k, n >= 0, k >= 1. Cf. A051126, A051127, A051777. - David Wasserman, Oct 01 2008 A051731(n,k) = A000007(T(n,k)). - Reinhard Zumkeller, Nov 01 2009 LINKS Alois P. Heinz, Rows n = 1..141, flattened Michael Z. Spivey, The Humble Sum of Remainders Function, Mathematics Magazine, Vol. 78, No. 4 (Oct., 2005), pp. 300-305. Weisstein, Eric W., Mod FORMULA T(n,k) = n - k * A010766(n,k). - Mats Granvik, Gary W. Adamson, Feb 20 2010 EXAMPLE 0 ; 0  0 ; 0  1  0 ; 0  0  1  0 ; 0  1  2  1  0 ; 0  0  0  2  1  0 ; 0  1  1  3  2  1  0 ; 0  0  2  0  3  2  1  0 ; 0  1  0  1  4  3  2  1  0 ; 0  0  1  2  0  4  3  2  1  0 ; 0  1  2  3  1  5  4  3  2  1  0 ; 0  0  0  0  2  0  5  4  3  2  1  0 ; ... From Omar E. Pol, Feb 21 2014: (Start) Illustration of the 12th row of triangle: ----------------------------------- .      k: 1 2 3 4 5 6 7 8 9 10..12 ----------------------------------- .         _ _ _ _ _ _ _ _ _ _ _ _ .        |_| | | | | | | | | | | | .        |_|_| | | | | | | | | | | .        |_| |_| | | | | | | | | | .        |_|_| |_| | | | | | | | | .        |_| | | |_| | | | | | | | .        |_|_|_| | |_| | | | | | | .        |_| | | | | |_| | | | | | .        |_|_| |_| | |*|_| | | | | .        |_| |_| | | |* *|_| | | | .        |_|_| | |_| |* * *|_| | | .        |_| | | |*| |* * * *|_| | .        |_|_|_|_|*|_|* * * * *|_| . Row 12 is 0 0 0 0 2 0 5 4 3 2 1 0 . (End) MAPLE T:= (n, k)-> modp(n, k): seq(seq(T(n, k), k=1..n), n=1..20); # Alois P. Heinz, Apr 04 2012 MATHEMATICA Flatten[Table[Mod[n, Range[n]], {n, 15}]] PROG (Haskell) a048158 = mod a048158_row n = a048158_tabl !! (n-1) a048158_tabl = zipWith (map . mod) [1..] a002260_tabl -- Reinhard Zumkeller, Apr 29 2015, Jan 20 2014 (fixed), Aug 13 2013 CROSSREFS Row sums are given by A004125. Cf. A002260. Cf. A000007, A010766, A051126, A051127, A051731, A051777. Sequence in context: A112207 A112208 A339089 * A275342 A246838 A219479 Adjacent sequences:  A048155 A048156 A048157 * A048159 A048160 A048161 KEYWORD nonn,tabl AUTHOR EXTENSIONS More terms from David Wasserman, Oct 01 2008 STATUS approved

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Last modified July 30 03:54 EDT 2021. Contains 346347 sequences. (Running on oeis4.)