A391451 Numbers k such that omega(k) = omega(d + k/d) for some divisor d of k and omega = A001221.

2, 3, 4, 7, 8, 14, 16, 20, 21, 24, 26, 31, 33, 34, 35, 36, 38, 39, 40, 44, 45, 48, 50, 51, 52, 54, 55, 56, 57, 62, 63, 64, 65, 68, 69, 72, 74, 75, 76, 77, 80, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 98, 99, 100, 104, 106, 108, 111, 112, 115, 116, 117, 118, 119, 122, 123, 124, 127

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

8 is a term because omega(8) = omega(1 + 8/1) = 1.

Maple

filter:= proc(k) local t, d;
  t:= NumberTheory:-Omega(k, distinct);
  ormap(d -> d^2 <= k and NumberTheory:-Omega(d+k/d, distinct)=t, NumberTheory:-Divisors(k))
end proc:
select(filter, [$1..200]); # Robert Israel, May 14 2026

Mathematica

q[k_] := AnyTrue[Divisors[k], PrimeNu[# + k/#] == PrimeNu[k] &]; Select[Range[128], q] (* Amiram Eldar, Dec 14 2025 *)

Prog

(PARI) is_a391451(n)=my(o=omega(n)); fordiv(n, d, if(omega(d+n\d)==o, return(1))); 0 \\ Hugo Pfoertner, Dec 14 2025

Crossrefs

Cf. A000005, A000668, A001221, A343733.

Sequence in context: A202116 A215914 A381544 * A006049 A084541 A240690

Adjacent sequences: A391448 A391449 A391450 * A391452 A391453 A391454

Keyword

nonn

Author

Juri-Stepan Gerasimov, Dec 09 2025

Status

approved