A336225 Table read by antidiagonals: T(n, k) = digitsum(n*k) with n >= 0 and k >= 0.

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, 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, 9, 6, 10, 3, 3, 10, 6, 9, 1, 0, 0, 2, 2, 9, 5, 8, 9, 8, 5, 9, 2, 2, 0

Offset

0,8

Links

Table of n, a(n) for n=0..90.

Index entries for sequences related to sum of digits.

Formula

T(n, k) = A007953(A004247(n, k)).

T(n, 1) = T(1, n) = A007953(n).

T(n, 2) = T(2, n) = A004092(n).

T(n, k) = A007953(A003991(n, k)) for n*k > 0. - Michel Marcus, Jul 13 2020.

Example

The table T(n, k) begins
0   0   0   0   0   0   0   0 ...
0   1   2   3   4   5   6   7 ...
0   2   4   6   8   1   3   5 ...
0   3   6   9   3   6   9   3 ...
0   4   8   3   7   2   6  10 ...
0   5   1   6   2   7   3   8 ...
0   6   3   9   6   3   9   6 ...
0   7   5   3  10   8   6  13 ...
...

Mathematica

T[n_, k_]:=Total[IntegerDigits[n*k]]; Table[T[n-k, k], {n, 0, 12}, {k, 0, n}]//Flatten

Prog

(PARI) T(n, k) = sumdigits(n*k);

Crossrefs

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).

Sequence in context: A067138 A059692 A353109 * A004247 A271916 A327031

Adjacent sequences: A336222 A336223 A336224 * A336226 A336227 A336228

Keyword

nonn,base,tabl,easy

Author

Stefano Spezia, Jul 12 2020

Status

approved