A215619 a(n) is the number of consecutive terms of A100071, beginning with index n, which are divisible by n.

4, 1, 6, 1, 8, 1, 4, 1, 12, 5, 14, 1, 4, 1, 18, 1, 20, 1, 4, 1, 24, 1, 6, 1, 4, 1, 30, 21, 32, 1, 12, 1, 8, 1, 38, 1, 14, 1, 42, 1, 44, 1, 6, 1, 48, 1, 8, 1, 4, 1, 54, 1, 6, 9, 4, 1, 60, 1, 62, 1, 4, 1, 6, 1, 68, 1, 4, 1, 72, 1, 74, 1, 4, 1, 12, 1, 80, 1, 4, 1

Offset: 3

Author

Vladimir Shevelev, Aug 17 2012

Keywords

• nonn

Comments

a(n) = n+1 iff n is prime.

a(n) = 1 iff n in { A067315 }.

1 <= a(n) <= n+1.

{ n : a(2n)>1 } = { A058008 } \ { 1 }.

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..1000

Crossrefs

Cf. A000040, A067315, A100071.

Programs

Maple

b:= proc(n) b(n):= n * binomial(n-1, floor((n-1)/2)) end:
a:= proc(n) local k;
      for k from 0 while irem(b(n+k), n)=0 do od; k
    end:
seq (a(n), n=3..100);  # Alois P. Heinz, Aug 17 2012

Mathematica

b[n_] := n Binomial[n-1, Floor[(n-1)/2]];
a[n_] := Module[{k = 0}, While[Mod[b[n+k], n] == 0, k++]; k];
a /@ Range[3, 100] (* Jean-François Alcover, Nov 22 2020, after Alois P. Heinz *)