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%I #26 Aug 21 2020 22:52:10
%S 0,0,0,0,1,0,0,2,2,0,0,3,4,3,0,0,4,6,6,4,0,0,5,8,9,8,5,0,0,6,1,3,3,1,
%T 6,0,0,7,3,6,7,6,3,7,0,0,8,5,9,2,2,9,5,8,0,0,9,7,3,6,7,6,3,7,9,0,0,1,
%U 9,6,10,3,3,10,6,9,1,0,0,2,2,9,5,8,9,8,5,9,2,2,0
%N Table read by antidiagonals: T(n, k) = digitsum(n*k) with n >= 0 and k >= 0.
%H <a href="/index/Su#sum_of_digits">Index entries for sequences related to sum of digits</a>.
%F T(n, k) = A007953(A004247(n, k)).
%F T(n, 1) = T(1, n) = A007953(n).
%F T(n, 2) = T(2, n) = A004092(n).
%F T(n, k) = A007953(A003991(n, k)) for n*k > 0. - _Michel Marcus_, Jul 13 2020.
%e The table T(n, k) begins
%e 0 0 0 0 0 0 0 0 ...
%e 0 1 2 3 4 5 6 7 ...
%e 0 2 4 6 8 1 3 5 ...
%e 0 3 6 9 3 6 9 3 ...
%e 0 4 8 3 7 2 6 10 ...
%e 0 5 1 6 2 7 3 8 ...
%e 0 6 3 9 6 3 9 6 ...
%e 0 7 5 3 10 8 6 13 ...
%e ...
%t T[n_,k_]:=Total[IntegerDigits[n*k]]; Table[T[n-k,k],{n,0,12},{k,0,n}]//Flatten
%o (PARI) T(n, k) = sumdigits(n*k);
%Y Cf. A003991, A004092, A004159 (diagonal), A004164 (digitsum of n^3), A004247, A007953, A055565 (digitsum of n^4), A055566 (digitsum of n^5), A055567 (digitsum of n^6).
%K nonn,base,tabl,easy
%O 0,8
%A _Stefano Spezia_, Jul 12 2020