cp's OEIS Frontend

A379693 a(n) is the least number k that has exactly n divisors <= sqrt(k) of the form 4*j+1.

%I A379693 #5 Dec 30 2024 02:17:55
%S A379693 1,25,90,585,1575,2475,5850,9945,16380,20475,36855,45045,69615,122850,
%T A379693 135135,176715,218295,225225,495495,405405,348075,696150,675675,
%U A379693 765765,1461915,1351350,2304225,1576575,4037670,2027025,2837835,2297295,4542615,4594590,5135130,3828825,6912675,5360355,8558550
%N A379693 a(n) is the least number k that has exactly n divisors <= sqrt(k) of the form 4*j+1.
%C A379693 a(n) is the least number k such that A364358(k) = n.
%C A379693 a(n) exists for every n, in fact A364358(5^(2*n-2)) = n.
%e A379693 a(3) = 90 because 90 has 3 divisors <= sqrt(90) of the form 4*j+1, namely 1, 5 and 9, and no smaller number works.
%p A379693 N:= 90: # for a(0) .. a(N)
%p A379693 f:= proc(n) nops(select(t -> t mod 4 = 1 and t^2 <= n, numtheory:-divisors(n))) end proc:
%p A379693 V:= Array(0..N): count:= 0:
%p A379693 for n from 1 while count < N+1 do
%p A379693   v:= f(n);
%p A379693   if v <= N and V[v] = 0 then V[v]:= n; count:= count+1 fi;
%p A379693 od:
%p A379693 convert(V, list);
%Y A379693 Cf. A364358, A379683.
%K A379693 nonn
%O A379693 1,2
%A A379693 _Robert Israel_, Dec 29 2024