A390251 Numbers k such that sigma(k) = psi(k) + omega(k)^2.

1, 4, 9, 12, 25, 49, 75, 121, 147, 169, 289, 361, 363, 507, 529, 841, 867, 961, 1083, 1369, 1587, 1681, 1849, 2209, 2523, 2809, 2883, 3481, 3721, 4107, 4489, 5041, 5043, 5329, 5547, 6241, 6627, 6889, 7921, 8427, 9409, 10201, 10443, 10609, 11163, 11449, 11881, 12769, 13467, 15123, 15987, 16129, 17161

Offset

1,2

Links

Table of n, a(n) for n=1..53.

Example

12 is in the sequence since sigma(12) = 28 = 24 + 2^2 = psi(12) + omega(12)^2.

Mathematica

psi[n_] := n * Times @@ (1 + 1/FactorInteger[n][[;; , 1]]); psi[1] = 1; Select[Range[18000], DivisorSigma[1, #] == psi[#] + PrimeNu[#]^2 &] (* Amiram Eldar, Oct 30 2025 *)

Crossrefs

Cf. A000203 (sigma), A001615 (psi), A001221 (omega).

Cf. A387953, A387999, A389478, A390252, A390253.

Sequence in context: A254520 A344578 A283105 * A179808 A083351 A055381

Adjacent sequences: A390248 A390249 A390250 * A390252 A390253 A390254

Keyword

nonn

Author

S. I. Dimitrov, Oct 30 2025

Status

approved