A058080 Numbers whose product of divisors exceeds their square.

12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 63, 64, 66, 68, 70, 72, 75, 76, 78, 80, 81, 84, 88, 90, 92, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 116, 117, 120, 124, 126, 128, 130, 132, 135, 136, 138, 140, 144, 147

Offset: 1

Author

N. J. A. Sloane, Nov 24 2000

Keywords

• nonn

Comments

Numbers with five or more divisors. - Lekraj Beedassy, Sep 11 2003

Called multiplicatively abundant numbers by Chau (2004). - Amiram Eldar, Jun 29 2022

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• William Chau, The tau, sigma, rho functions, and some related numbers, Pi Mu Epsilon Journal, Vol. 11, No. 10 (Spring 2004), pp. 519-534; entire issue.

Crossrefs

Complement of A007964.

Cf. A000430, A007422, A007955.

Programs

Mathematica

Select[Range[150], #^(DivisorSigma[0, #]/2) > #^2 &] (* Amiram Eldar, Jun 29 2022 *)
Select[Range[200],Times@@Divisors[#]>#^2&] (* Harvey P. Dale, Oct 20 2024 *)

PARI

is(n)=numdiv(n)>4 \\ Charles R Greathouse IV, Sep 18 2015

Python

from sympy import divisor_count
def ok(n): return divisor_count(n) > 4
print([k for k in range(148) if ok(k)]) # Michael S. Branicky, Dec 16 2021

Formula

The number of terms not exceeding x is N(x) ~ x*(1 - log(log(x))/log(x)) (Chau, 2004). - Amiram Eldar, Jun 29 2022