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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
OFFSET
1,9
COMMENTS
9 divides all terms, which shows the "casting out nines" congruence of multiplication.
LINKS
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)
Triangle:
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: A377694 A090655 A334480 * A076115 A014726 A277069
KEYWORD
nonn,base,tabl
AUTHOR
STATUS
approved