A392507 Numbers k such that the abundancy index of sigma(k) divided by the abundancy index of d(k) equals a whole number.

1, 12, 90, 2878, 3118, 3595, 3949, 4063, 4117, 4183, 4187, 4189, 4279, 4427, 18716, 19653, 24323, 25093, 25813, 25853, 63984, 156664, 163190, 171346, 183585, 187634, 191666, 192826, 193234, 193486, 194438, 194578, 208029, 209247, 212889, 216471, 217047, 217857, 218697

Offset

1,2

Comments

Includes the sublime numbers.

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..3879

Example

12 has sigma(12) = 28, and d(12) = 6, and sigma(28)/28 = 2 and sigma(6)/6 = 2, thus 2/2 = 1.
4117 has sigma(4117) = 4320, and d(4117) = 4, and sigma(4320)/4320 = 7/2 and sigma(4)/4 = 7/4 and 7/2 divided by 7/4 is 2.

Mathematica

fQ[n_] := IntegerQ[ Divide @@ DivisorSigma[-1, DivisorSigma[{1, 0}, n]]]; Select[Range[220000], fQ] (* Amiram Eldar, Jan 14 2026 *) (* slightly modified by Robert G. Wilson v, Jan 25 2026 for speed *)

Prog

(PARI) isok(k) = denominator(sigma(sigma(k), -1)/sigma(numdiv(k), -1)) == 1; \\ Michel Marcus, Jan 15 2026

Crossrefs

Cf. A081357, A000203, A000005.

Cf. A392506 (a subsequence).

Sequence in context: A231512 A250344 A135173 * A173223 A392506 A114860

Adjacent sequences: A392504 A392505 A392506 * A392508 A392509 A392510

Keyword

nonn

Author

Leo Hennig, Jan 14 2026

Extensions

More terms from Amiram Eldar, Jan 14 2026

Status

approved