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A073804 Numbers k such that the number of divisors of k is greater than that of sigma(k).

%I A073804 #19 Mar 07 2025 02:56:02
%S A073804 4,9,16,18,25,36,48,50,64,72,80,81,100,112,144,162,180,192,196,200,
%T A073804 208,225,240,252,256,288,289,300,320,324,336,400,432,441,448,450,468,
%U A073804 484,512,576,578,592,624,625,648,676,700,704,720,729,768,784,800,810,832
%N A073804 Numbers k such that the number of divisors of k is greater than that of sigma(k).
%H A073804 Amiram Eldar, <a href="/A073804/b073804.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%F A073804 Solutions to A000005(x) > A062068(x) = A000005(A000203(x)).
%e A073804 k = 25: divisors(25) = {1,5,25}, 3 divisors; divisors(sigma(25)) = {1,31}, 2 divisors; 2 < 3, so 25 is a term.
%e A073804 k = 48: divisors(48) = {1,2,3,4,6,8,12,16,24,48}, 10 divisors; divisors(sigma(48)) = {1,2,4,31,62,124}, 6 divisors, 6 < 10 so 48 is a term.
%t A073804 Do[s=DivisorSigma[0, DivisorSigma[1, n]]; s0=DivisorSigma[0, n]; If[Greater[s0, s], Print[n]], {n, 1, 1000}]
%t A073804 Select[Range[900],DivisorSigma[0,#]>DivisorSigma[0,DivisorSigma[1,#]]&] (* _Harvey P. Dale_, Jan 18 2017 *)
%o A073804 (PARI) isok(k) = {my(f = factor(k)); numdiv(f) > numdiv(sigma(f));} \\ _Amiram Eldar_, Mar 07 2025
%Y A073804 Cf. A000005, A000203, A062068, A073802, A073803, A037197.
%K A073804 nonn
%O A073804 1,1
%A A073804 _Labos Elemer_, Aug 13 2002