This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A219019 #32 Mar 27 2025 11:48:32
%S A219019 3,4,7,8,16,11,79,44,81,91,1024,47,12769,389,256,413,46656,373,
%T A219019 1048576,1000,4096,43541
%N A219019 Smallest number k > 1 such that k^n - 1 contains n distinct prime divisors.
%C A219019 365000 < a(19) <= 1048576; a(20) = 1000; a(21) = 4096; a(22) = 43541. - _Daniel Suteu_, Jul 10 2022
%e A219019 a(3) = 7 is the smallest number of the set {k(i)} = {7, 9, 13, 15, 19, 21, ...} where k(i)^3 - 1 contains 3 distinct prime divisors.
%p A219019 with(numtheory) :for n from 1 to 10 do:ii:=0:for k from 1 to 10^10 while(ii=0) do:x:=k^n-1:y:=factorset(x):n1:=nops(y):if n1=n then ii:=1: printf ( "%d %d \n",n,k):
%p A219019 else fi:od:od:
%t A219019 L = {}; Do[n = 1; While[Length[FactorInteger[n^k - 1]] != k, n++]; Print@AppendTo[L, n], {k, 15}] (* _Giovanni Resta_, Nov 10 2012 *)
%t A219019 snk[n_]:=Module[{k=2},While[PrimeNu[k^n-1]!=n,k++];k]; Array[snk,22] (* _Harvey P. Dale_, Mar 27 2025 *)
%o A219019 (PARI) a(n) = my(k=2); while (omega(k^n-1) != n, k++); k; \\ _Daniel Suteu_, Jul 10 2022
%Y A219019 Cf. A001221, A359070.
%K A219019 nonn,more,hard
%O A219019 1,1
%A A219019 _Michel Lagneau_, Nov 09 2012
%E A219019 a(13)-a(18), a(20)-a(22) from _Daniel Suteu_, Jul 10 2022
%E A219019 a(19) from _Jinyuan Wang_, Feb 13 2023