A340260 T(n, k) = Sum_{j=1..k} [n mod j <> 1], where [] is the Iverson bracket. Table read by rows.

1, 1, 2, 1, 1, 2, 1, 2, 2, 3, 1, 1, 2, 2, 3, 1, 2, 3, 4, 4, 5, 1, 1, 1, 2, 3, 3, 4, 1, 2, 3, 4, 5, 6, 6, 7, 1, 1, 2, 2, 3, 4, 5, 5, 6, 1, 2, 2, 3, 4, 5, 6, 7, 7, 8, 1, 1, 2, 3, 3, 4, 5, 6, 7, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 11, 1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 7, 7, 8

Offset: 1

Author

Peter Luschny, Jan 02 2021

Keywords

• nonn
• tabl

Examples

			Table starts:
                             [1] 1;
                           [2] 1, 2;
                          [3] 1, 1, 2;
                        [4] 1, 2, 2, 3;
                       [5] 1, 1, 2, 2, 3;
                     [6] 1, 2, 3, 4, 4, 5;
                    [7] 1, 1, 1, 2, 3, 3, 4;
                  [8] 1, 2, 3, 4, 5, 6, 6, 7;
                 [9] 1, 1, 2, 2, 3, 4, 5, 5, 6;
               [10] 1, 2, 2, 3, 4, 5, 6, 7, 7, 8.
		

Crossrefs

T(n, n) = n + 1 - tau(n-1) for n >= 2.

Cf. A000005, A051731, A243987, A340261.

Programs

Maple

IversonBrackets := expr -> subs(true=1, false=0, evalb(expr)):
T := (n, k) -> add(IversonBrackets(irem(n, j) <> 1), j = 1..k):
for n from 1 to 19 do seq(T(n, k), k = 1..n) od;