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
Examples
a(3) = 16 because 16 has exactly 3 divisors that are not balanced numbers, namely 4, 8 and 16, and no smaller number works.
Links
- David A. Corneth, Table of n, a(n) for n = 0..752 (first 251 terms from Robert Israel)
Programs
-
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);
-
PARI
a(n) = my(k=1); while (sumdiv(k, d, sigma(d)%eulerphi(d) != 0) != n, k++); k; \\ Michel Marcus, Aug 26 2025
Comments