cp's OEIS Frontend

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

%I A090525 #15 Mar 20 2023 16:06:52
%S A090525 2,2,11,9,11,20,10,42,13,16,57,7,35,41,53,35,171,18,141,45,19,55,212,
%T A090525 236,94,265,13,76,26,9,13,21,160,21,21,24,378,100,66,52,75,54,214,6,
%U A090525 678,193,137,123,138,59,605,87,165,109,417,403,100,57,778,719,79,12,83,450
%N A090525 Least number k such that floor((n^n)/k) is prime, or 0 if no such number exists.
%C A090525 Conjecture: No term is zero.
%C A090525 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
%H A090525 Robert Israel, <a href="/A090525/b090525.txt">Table of n, a(n) for n = 2..577</a>
%p A090525 f:= proc(n) local t,k;
%p A090525   t:= n^n;
%p A090525   for k from 2 do if isprime(floor(t/k)) then return k fi od
%p A090525 end proc:
%p A090525 map(f, [$2..100]); # _Robert Israel_, Mar 02 2023
%t A090525 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 *)
%o A090525 (PARI) a(n)=for(i=1,1000,if(isprime(floor((n^n)/i)),print1(i,",");break()))
%Y A090525 Cf. A090526, A090527, A090528.
%K A090525 nonn
%O A090525 2,1
%A A090525 _Amarnath Murthy_, Dec 07 2003