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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.)