A396049 a(n) is the least number k that has exactly n divisors d <= sqrt(k) such that omega(d + k/d) = omega(k), where omega = A001221.

1, 2, 4, 36, 108, 96, 144, 288, 972, 1152, 2304, 5400, 4320, 14000, 14256, 12096, 7056, 12960, 24192, 17280, 48384, 54000, 62720, 43200, 69120, 51840, 116640, 72000, 194400, 127008, 465696, 207360, 259200, 622080, 345600, 933120, 864000, 508032, 518400, 870912, 777600, 1617408

Offset

0,2

Links

Table of n, a(n) for n=0..41.

Example

a(4) = 108 because omega(108) = 2 (as 108 = 2^2 * 3^3), there are 4 divisors d of 108 with d <= sqrt(108) and omega(d + 108/d) = 2, namely d=2 with 2+108/2 = 56 = 2^3 * 7, d=3 with 3+108/3 = 39 = 3*13, d=6 with 6+108/6 = 24 = 3*2^3, and d=9 with 9+108/9 = 21 = 3*7, and 108 is the least number that works.

Maple

g:= proc(k) local t; uses NumberTheory;
  t:= Omega(k, distinct);
  nops(select(d -> d^2 <= k and Omega(d+k/d, distinct)=t, Divisors(k)))
end proc:
V:= Array(0..40): count:= 0:
for x from 1 while count < 41 do
  v:= g(x);
  if v<= 40 and V[v]=0 then V[v]:= x; count:= count+1 fi
od:
convert(V, list);

Mathematica

a[n_]:=Module[{k=1}, While[Length[Select[Divisors[k], #<=Sqrt[k] && PrimeNu[#+k/#]==PrimeNu[k] &]]!=n, k++]; k]; Array[a, 20, 0] (* Stefano Spezia, May 14 2026 *)

Prog

(PARI) isok(k, n) = my(s=sqrt(k), o=omega(k)); sumdiv(k, d, (d<=s) && (omega(d+k/d)==o)) == n;
a(n) = my(k=1); while(!isok(k, n), k++); k; \\ Michel Marcus, May 16 2026

Crossrefs

Cf. A001221, A391451.

Sequence in context: A383086 A009090 A009295 * A277091 A199495 A182965

Adjacent sequences: A396046 A396047 A396048 * A396050 A396052 A396053

Keyword

nonn

Author

Robert Israel, May 14 2026

Status

approved