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

1,1

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.

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

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 *)

Prog

(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

Crossrefs

Complement of A007964.

Cf. A000430, A007422, A007955.

Sequence in context: A068394 A189685 A126763 * A119911 A272861 A192690

Adjacent sequences: A058077 A058078 A058079 * A058081 A058082 A058083

Keyword

nonn

Author

N. J. A. Sloane, Nov 24 2000

Status

approved