A090525 Least number k such that floor((n^n)/k) is prime, or 0 if no such number exists.

2, 2, 11, 9, 11, 20, 10, 42, 13, 16, 57, 7, 35, 41, 53, 35, 171, 18, 141, 45, 19, 55, 212, 236, 94, 265, 13, 76, 26, 9, 13, 21, 160, 21, 21, 24, 378, 100, 66, 52, 75, 54, 214, 6, 678, 193, 137, 123, 138, 59, 605, 87, 165, 109, 417, 403, 100, 57, 778, 719, 79, 12, 83, 450

Offset: 2

Author

Amarnath Murthy, Dec 07 2003

Keywords

• nonn

Comments

Conjecture: No term is zero.

The conjecture is true: If p is a prime factor of n, k = (n^n)/p gives an upper bound. - James Rayman, Mar 01 2023

Links

• Robert Israel, Table of n, a(n) for n = 2..577

Crossrefs

Cf. A090526, A090527, A090528.

Programs

Maple

f:= proc(n) local t,k;
  t:= n^n;
  for k from 2 do if isprime(floor(t/k)) then return k fi od
end proc:
map(f, [$2..100]); # Robert Israel, Mar 02 2023

Mathematica

lnk[n_]:=Module[{k=1,nn=n^n},While[!PrimeQ[Floor[nn/k]],k++];k]; Array[lnk,70,2] (* Harvey P. Dale, Nov 07 2022 *)

PARI

a(n)=for(i=1,1000,if(isprime(floor((n^n)/i)),print1(i,",");break()))