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 A229758 Triangle T(n,k) = A007953(n) * A007953(k) - A007953(n*k) with 1 <= k <= n. 1
 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 0, 9, 9, 18, 18, 0, 9, 9, 18, 27, 27, 0, 9, 18, 18, 27, 36, 36, 0, 9, 18, 27, 36, 36, 45, 54, 0, 9, 18, 27, 36, 45, 54, 63, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 18, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 COMMENTS 9 divides all terms, which shows the "casting out nines" congruence of multiplication. LINKS Indranil Ghosh, Rows 1..120 of triangle, flattened Eric Weisstein's World of Mathematics, Casting Out Nines Eric Weisstein's World of Mathematics, Digit Sum Wikipedia, Digit sum EXAMPLE From Indranil Ghosh, Feb 14 2017, (Start) Table: 1:   0, 2:   0,  0, 3:   0,  0, 0, 4:   0,  0, 9,  9, 5:   0,  9, 9,  18, 18, 6:   0,  9, 9,  18, 27, 27, 7:   0,  9, 18, 18, 27, 36, 36, 8:   0,  9, 18, 27, 36, 36, 45, 54, 9:   0,  9, 18, 27, 36, 45, 54, 63, 72, 10:  0,  0, 0,  0,  0,  0,  0,  0,  0,  0, 11:  0,  0, 0,  0,  0,  0,  0,  0,  0,  0, 0, 12:  0,  0, 0,  0,  9,  9,  9,  9,  18, 0, 0, 0, ... T(12,5) = A007953(12) * A007953(5) - A007953(12 * 5) = 3 * 5 - 6 = 15 - 6 = 9. (End) MATHEMATICA dSum[n_] := Total[IntegerDigits[n]]; Flatten[Table[dSum[n]*dSum[k] - dSum[n*k], {n, 12}, {k, n}]] (* T. D. Noe, Oct 01 2013 *) CROSSREFS Cf. A007953. Sequence in context: A324859 A090655 A334480 * A076115 A014726 A277069 Adjacent sequences:  A229755 A229756 A229757 * A229759 A229760 A229761 KEYWORD nonn,base,tabl AUTHOR Enrique Pérez Herrero, Sep 28 2013 STATUS approved

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)