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

1, 25, 90, 585, 1575, 2475, 5850, 9945, 16380, 20475, 36855, 45045, 69615, 122850, 135135, 176715, 218295, 225225, 495495, 405405, 348075, 696150, 675675, 765765, 1461915, 1351350, 2304225, 1576575, 4037670, 2027025, 2837835, 2297295, 4542615, 4594590, 5135130, 3828825, 6912675, 5360355, 8558550

Offset: 1

Author

Robert Israel, Dec 29 2024

Keywords

• nonn

Comments

a(n) is the least number k such that A364358(k) = n.

a(n) exists for every n, in fact A364358(5^(2*n-2)) = n.

Examples

			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.
		

Crossrefs

Cf. A364358, A379683.

Programs

Maple

N:= 90: # for a(0) .. a(N)
f:= proc(n) nops(select(t -> t mod 4 = 1 and t^2 <= n, numtheory:-divisors(n))) end proc:
V:= Array(0..N): count:= 0:
for n from 1 while count < N+1 do
  v:= f(n);
  if v <= N and V[v] = 0 then V[v]:= n; count:= count+1 fi;
od:
convert(V, list);