cp's OEIS Frontend

A058080 Numbers whose product of divisors exceeds their square.

%I A058080 #31 Oct 20 2024 16:25:27
%S A058080 12,16,18,20,24,28,30,32,36,40,42,44,45,48,50,52,54,56,60,63,64,66,68,
%T A058080 70,72,75,76,78,80,81,84,88,90,92,96,98,99,100,102,104,105,108,110,
%U A058080 112,114,116,117,120,124,126,128,130,132,135,136,138,140,144,147
%N A058080 Numbers whose product of divisors exceeds their square.
%C A058080 Numbers with five or more divisors. - _Lekraj Beedassy_, Sep 11 2003
%C A058080 Called multiplicatively abundant numbers by Chau (2004). - _Amiram Eldar_, Jun 29 2022
%H A058080 Charles R Greathouse IV, <a href="/A058080/b058080.txt">Table of n, a(n) for n = 1..10000</a>
%H A058080 William Chau, <a href="https://www.jstor.org/stable/24340619">The tau, sigma, rho functions, and some related numbers</a>, Pi Mu Epsilon Journal, Vol. 11, No. 10 (Spring 2004), pp. 519-534; <a href="http://www.pme-math.org/journal/issues/PMEJ.Vol.11.No10.pdf">entire issue</a>.
%F A058080 The number of terms not exceeding x is N(x) ~ x*(1 - log(log(x))/log(x)) (Chau, 2004). - _Amiram Eldar_, Jun 29 2022
%t A058080 Select[Range[150], #^(DivisorSigma[0, #]/2) > #^2 &] (* _Amiram Eldar_, Jun 29 2022 *)
%t A058080 Select[Range[200],Times@@Divisors[#]>#^2&] (* _Harvey P. Dale_, Oct 20 2024 *)
%o A058080 (PARI) is(n)=numdiv(n)>4 \\ _Charles R Greathouse IV_, Sep 18 2015
%o A058080 (Python)
%o A058080 from sympy import divisor_count
%o A058080 def ok(n): return divisor_count(n) > 4
%o A058080 print([k for k in range(148) if ok(k)]) # _Michael S. Branicky_, Dec 16 2021
%Y A058080 Complement of A007964.
%Y A058080 Cf. A000430, A007422, A007955.
%K A058080 nonn
%O A058080 1,1
%A A058080 _N. J. A. Sloane_, Nov 24 2000