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A378592 a(n) is the first number that is the largest primitive root modulo exactly n numbers.

%I A378592 #4 Dec 03 2024 12:26:24
%S A378592 4,1,3,47,5
%N A378592 a(n) is the first number that is the largest primitive root modulo exactly n numbers.
%C A378592 a(n) is the first number that occurs exactly n times in A306253.
%C A378592 Is there any number that occurs more than 4 times in A306253?
%e A378592 4 is not the largest primitive root mod any number.
%e A378592 1 is the largest primitive root mod 2.
%e A378592 3 is the largest primitive root mod 4 and mod 5.
%e A378592 47 is the largest primitive root mod 49, 50, and 54.
%e A378592 5 is the largest primitive root mod 6, 7, 9, and 14.
%p A378592 f:= proc(b) local x, t;
%p A378592   t:= numtheory:-phi(b);
%p A378592   for x from b-1 by -1 do if igcd(x, b) = 1 and numtheory:-order(x, b)=t then return x fi od
%p A378592 end proc:
%p A378592 f(1):= 0:
%p A378592 cands:= select(t -> t=1 or numtheory:-primroot(t) <> FAIL, [$1..1000]):
%p A378592 R:= map(f, cands):
%p A378592 S:= sort(convert(convert(R,set),list)):
%p A378592 V:= Array(0..10): V[0]:= 4:
%p A378592 for s in S do
%p A378592   v:= numboccur(s,R);
%p A378592   if  V[v] = 0 then V[v]:= s fi
%p A378592 od:
%p A378592 convert(V,list); # _Robert Israel_, Dec 01 2024
%Y A378592 Cf. A306253.
%K A378592 nonn,more
%O A378592 0,1
%A A378592 _Robert Israel_, Dec 01 2024