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

2,1

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

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 *)

Prog

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

Crossrefs

Cf. A090526, A090527, A090528.

Sequence in context: A213990 A275429 A222878 * A328455 A265530 A309477

Adjacent sequences: A090522 A090523 A090524 * A090526 A090527 A090528

Keyword

nonn

Author

Amarnath Murthy, Dec 07 2003

Status

approved