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A058080 Numbers whose product of divisors exceeds their square. 9
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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

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Last modified October 2 15:42 EDT 2022. Contains 357226 sequences. (Running on oeis4.)