A388268 Numbers k for which A000005(k) >= A017665(k), where A000005 is the number of divisors function, and A017665 is the numerator of the abundancy ratio, sigma(k)/k.

1, 6, 24, 28, 84, 120, 140, 224, 234, 270, 360, 420, 496, 672, 840, 1080, 1170, 1488, 1638, 2016, 2160, 2480, 2520, 2970, 3276, 3360, 3472, 3724, 3780, 3960, 4320, 4464, 4680, 5400, 6048, 6200, 6552, 7392, 7440, 8128, 8190, 8736, 9504, 10080, 10296, 10920, 11172, 11466, 11880

Offset

1,2

Comments

Numbers k such that A388270(k) >= A000203(k).

After the initial 1, conjectured to be a subsequence of A023196. Note that for deficient numbers, k in A005100, we always have gcd(sigma(k),k) <= A032742(k), but not necessarily A000203(k) > A000005(k)*A032742(k).

Links

Antti Karttunen, Table of n, a(n) for n = 1..3333

Plot2 of A388270 vs. A000203 (stray black points above the red area occur at x-locations given by this sequence)

Formula

{k | A000203(k) <= A000005(k)*A009194(k)}.

Mathematica

OK[n_]:=If[DivisorSigma[0, n]>=Numerator[DivisorSigma[-1, n]], True]; Select[Range[12000], OK] (* James C. McMahon, Sep 20 2025 *)

Prog

(PARI) is_A388268(n) = { my(s=sigma(n)); ((s/gcd(n, s))<=numdiv(n)); };
(PARI) isok(k) = my(f=factor(k)); numdiv(f) >= numerator(sigma(f, -1)) \\ Michel Marcus, Sep 20 2025

Crossrefs

Cf. A000005, A000203, A009194, A017665, A032742, A388270.

Apparently, after 1, a subsequence of A023196.

Subsequences: A001599, A007691 (and all its subsequences like A000396, A005820, etc), A388269 (odd terms).

Sequence in context: A293453 A344754 A364977 * A336641 A336550 A118372

Adjacent sequences: A388265 A388266 A388267 * A388269 A388270 A388271

Keyword

nonn

Author

Antti Karttunen, Sep 19 2025

Status

approved