A387333 a(n) is the least k having exactly n divisors that are not balanced numbers.

1, 4, 8, 16, 20, 48, 40, 72, 80, 120, 144, 180, 320, 240, 440, 432, 540, 360, 792, 864, 900, 960, 1620, 720, 1080, 1920, 2808, 2016, 2340, 1440, 3168, 3024, 2160, 4032, 5616, 2880, 5940, 8100, 3600, 6048, 3960, 5040, 6480, 10920, 7560, 14112, 11700, 7200, 8640, 11880, 13104, 13680, 7920, 10080

Offset

0,2

Comments

a(n) is the least k such that A386591(k) = n.

Links

David A. Corneth, Table of n, a(n) for n = 0..752 (first 251 terms from Robert Israel)

Example

a(3) = 16 because 16 has exactly 3 divisors that are not balanced numbers, namely 4, 8 and 16, and no smaller number works.

Maple

g:= proc(n) option remember; numtheory:-sigma(n) mod numtheory:-phi(n) <> 0 end proc:
f:= n -> nops(select(g, numtheory:-divisors(n))):
N:= 60: # for a(0) to a(N)
V:= Array(0..N, -1): count:= 0:
for i from 1 while count < N+1 do
  v:= f(i);
  if V[v] = -1 then count:= count+1; V[v]:= i; fi
od:
convert(V, list);

Prog

(PARI) a(n) = my(k=1); while (sumdiv(k, d, sigma(d)%eulerphi(d) != 0) != n, k++); k; \\ Michel Marcus, Aug 26 2025

Crossrefs

Cf. A020492, A386591.

Sequence in context: A272753 A272804 A237990 * A335792 A312807 A312808

Adjacent sequences: A387330 A387331 A387332 * A387334 A387335 A387336

Keyword

nonn

Author

Robert Israel, Aug 26 2025

Status

approved