login
A090525
Least number k such that floor((n^n)/k) is prime, or 0 if no such number exists.
4
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
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
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Dec 07 2003
STATUS
approved