cp's OEIS Frontend

A379683 a(n) is the least number k that has exactly n divisors <= sqrt(k) of the form 4*j+3.

%I A379683 #6 Dec 30 2024 02:17:46
%S A379683 1,9,63,231,945,1890,3465,5775,12285,10395,20790,60060,45045,75075,
%T A379683 98175,103950,176715,135135,225225,270270,405405,900900,1060290,
%U A379683 810810,765765,675675,1354815,1351350,1711710,2702700,2027025,4542615,2297295,3378375,5360355,6216210,3828825,6774075,10270260
%N A379683 a(n) is the least number k that has exactly n divisors <= sqrt(k) of the form 4*j+3.
%C A379683 a(n) is the least number k such that A364387(k) = n.
%C A379683 a(n) exists for every n, in fact A364387(3^(4*n-2)) = n.
%e A379683 a(3) = 231 because 231 has exactly 3 divisors <= sqrt(231) of the form 4*j+3, namely 3, 7 and 11, and this is the least number that works.
%p A379683 N:= 90: # for a(0) .. a(N)
%p A379683 f:= proc(n) nops(select(t -> t mod 4 = 3 and t^2 <= n, numtheory:-divisors(n))) end proc:
%p A379683 V:= Array(0..N): count:= 0:
%p A379683 for n from 1 while count < N+1 do
%p A379683   v:= f(n);
%p A379683   if v <= N and V[v] = 0 then V[v]:= n; count:= count+1 fi;
%p A379683 od:
%p A379683 convert(V,list);
%Y A379683 Cf. A364387.
%K A379683 nonn
%O A379683 0,2
%A A379683 _Robert Israel_, Dec 29 2024