A293246 a(n) is the smallest k > 1 such that A000166(k) is divisible by n!.

2, 2, 3, 7, 25, 121, 241, 1681, 13441, 40321, 403201, 2016001, 3225601, 41932801, 609638401

Offset: 0

Author

Altug Alkan, Oct 03 2017

Keywords

• nonn
• more

Comments

a(n) is the smallest k > 1 such that round(k!/e) is divisible by n!.

Terms are 0! + 1, 1! + 1, 2! + 1, 3! + 1, 4! + 1, 5! + 1, 6!/3 + 1, 7!/3 + 1, ...

Examples

			a(3) = 7 because the smallest nonzero subfactorial number that is divisible by 3! is A000166(7) = 1854.
		

Crossrefs

Cf. A000142, A000166.

Programs

Maple

f:= proc(n) local k, t, p;
p:= n!;
t:= 0;
for k from 2 do
  t:= k*t + (-1)^k mod p;
  if t = 0 then return k fi
od:
end proc:
seq(f(n),n=0..13); # Robert Israel, Oct 03 2017

Extensions

a(8)-a(14) from Robert Israel, Oct 03 2017