A389634 Numbers k whose abundancy (sigma(k)/k) is at least 4/3, where sigma(k) = A000203(k).

2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 56, 57, 58, 60, 62, 63, 64, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 86, 87, 88, 90, 92, 93, 94, 96, 98, 99, 100

Offset

1,1

Comments

Complement of A389633. Numbers k such that 2k or 3k is nondeficient (see A023196).

The numbers of terms that do not exceed 10^k, for k = 1, 2, ..., are 7, 68, 680, 6804, 68133, 681454, 6813375, 68136924, 681370873, 6813622783, ... . Apparently, the asymptotic density of this sequence exists and equals 0.6813... . - Amiram Eldar, Nov 10 2025

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

q[k_] := DivisorSigma[-1, k] >= 4/3; Select[Range[100], q] (* Amiram Eldar, Oct 11 2025 *)

Prog

(PARI) isok(k) = (3*sigma(k) >= 4*k)

Crossrefs

Subsequences: A023196 (therefore A000396 and A005101), A047229\{0}, A388012.

Cf. A000203, A334117, A389635 (primitive terms).

Sequence in context: A353684 A377236 A377182 * A047229 A094229 A067290

Adjacent sequences: A389631 A389632 A389633 * A389635 A389636 A389637

Keyword

nonn,easy

Author

Peter Munn, Oct 11 2025

Status

approved