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A219364 Numbers such that the product of divisors of n is greater than the product of divisors of sigma(n).

%I A219364 #23 Jun 25 2022 11:32:12
%S A219364 4,9,16,18,25,36,48,50,64,72,80,81,100,112,144,162,192,200,208,225,
%T A219364 240,256,288,289,300,320,324,336,400,432,441,448,450,468,484,512,576,
%U A219364 578,592,624,625,648,676,704,720,729,768,784,800,832,882,900,960,976
%N A219364 Numbers such that the product of divisors of n is greater than the product of divisors of sigma(n).
%C A219364 That is, numbers satisfying A007955(n) > A007955(A000203(n)).
%H A219364 Vincenzo Librandi, <a href="/A219364/b219364.txt">Table of n, a(n) for n = 1..1000</a>
%H A219364 F. Luca, <a href="https://www.emis.de/journals/JIPAM/article284.html">On the product of divisors of n and sigma(n)</a>, J. Inequal. Pure Appl. Math., Volume 4, Issue 2, Article 46, 2003.
%t A219364 Select[Range[1000], Times @@ Divisors[#] > Times @@ Divisors[DivisorSigma[1, #]] &] (* _T. D. Noe_, Nov 19 2012 *)
%o A219364 (PARI) A007955(n)=if(issquare(n,&n),n^numdiv(n^2),n^(numdiv(n)/2))
%o A219364 is(n)=A007955(n)>A007955(sigma(n)) \\ _Charles R Greathouse IV_, Feb 04 2013
%o A219364 (Python)
%o A219364 from math import isqrt
%o A219364 from itertools import count, islice
%o A219364 from sympy import divisor_count, divisor_sigma
%o A219364 def A219364_gen(): # generator of terms
%o A219364     return filter(lambda n: (f:=(lambda m:isqrt(m)**c if (c:=divisor_count(m)) & 1 else m**(c//2)))(n) > f(divisor_sigma(n)),count(1))
%o A219364 A219364_list = list(islice(A219364_gen(),20)) # _Chai Wah Wu_, Jun 25 2022
%Y A219364 Cf. A000203, A007955.
%K A219364 nonn,easy
%O A219364 1,1
%A A219364 _Michel Marcus_, Nov 19 2012