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

1, 9, 63, 231, 945, 1890, 3465, 5775, 12285, 10395, 20790, 60060, 45045, 75075, 98175, 103950, 176715, 135135, 225225, 270270, 405405, 900900, 1060290, 810810, 765765, 675675, 1354815, 1351350, 1711710, 2702700, 2027025, 4542615, 2297295, 3378375, 5360355, 6216210, 3828825, 6774075, 10270260

Offset

0,2

Comments

a(n) is the least number k such that A364387(k) = n.

a(n) exists for every n, in fact A364387(3^(4*n-2)) = n.

Links

Table of n, a(n) for n=0..38.

Example

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.

Maple

N:= 90: # for a(0) .. a(N)
f:= proc(n) nops(select(t -> t mod 4 = 3 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);

Crossrefs

Cf. A364387.

Sequence in context: A344526 A269641 A269410 * A178161 A015669 A202982

Adjacent sequences: A379680 A379681 A379682 * A379684 A379685 A379686

Keyword

nonn

Author

Robert Israel, Dec 29 2024

Status

approved