A334117 Odd numbers with abundancy >= 3/2; that is, numbers m such that sigma(m) >= 3m/2.

15, 21, 45, 63, 75, 99, 105, 117, 135, 147, 153, 165, 171, 189, 195, 207, 225, 231, 255, 273, 285, 297, 315, 345, 351, 357, 375, 399, 405, 429, 435, 441, 459, 465, 483, 495, 513, 525, 555, 561, 567, 585, 609, 615, 621, 627, 645, 651, 663, 675, 693, 705, 735, 741, 759

Offset: 1

Author

Charles R Greathouse IV, Apr 14 2020

Keywords

• nonn

Comments

The density of this sequence exists and is positive. If m is in this sequence, then so is mk, where k is a positive odd number (see A334118).

The numbers of terms that do not exceed 10^k, for k = 2, 3, ..., are 6, 73, 700, 7179, 70759, 709928, 7101533, 70999783, 709865878, 7098956986, ... . Apparently, the asymptotic density of this sequence equals 0.0709... . - Amiram Eldar, Dec 28 2024

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A334118, A000203, A005231, A119240.

Programs

Mathematica

Select[Range[1, 1000, 2], DivisorSigma[-1, #] >= 3/2 &] (* Amiram Eldar, Dec 28 2024 *)

PARI

is(n)=n%2 && sigma(n,-1)>=3/2

PARI

forfactored(n=1,10^4, if(sigma(n,-1)>=3/2 && n[1]%2, print1(n[1]", ")))