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

1,3

Links

Table of n, a(n) for n=1..91.

Example

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.

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;

Crossrefs

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

Cf. A000005, A051731, A243987, A340261.

Sequence in context: A243987 A050205 A281530 * A175190 A317685 A257540

Adjacent sequences: A340257 A340258 A340259 * A340261 A340262 A340263

Keyword

nonn,tabl

Author

Peter Luschny, Jan 02 2021

Status

approved