This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A377563 #7 Nov 01 2024 23:51:24
%S A377563 16,36,48,80,81,100,112,144,162,176,180,196,208,225,240,252,256,272,
%T A377563 288,300,304,324,336,368,396,400,405,432,441,450,464,468,484,496,512,
%U A377563 528,560,567,576,588,592,612,624,625,648,656,676,684,688,700,720,752,768,784,800
%N A377563 Numbers that have fewer infinitary divisors than noninfinitary divisors.
%C A377563 Numbers whose prime factorization has at least one exponent that has at least two zeros in its binary representation (A158582), or at least two exponents that are not of the form 2^k-1, with k >= 1 (A062289).
%C A377563 The asymptotic density of this sequence is 1 - d * (1 + Sum_{p prime} (Sum_{k>=0} 1/p^(3*2^k-1))/(1 + Sum_{k>=1} 1/p^(2^k-1))) = 0.07306380398261191432..., where d = A327839.
%H A377563 Amiram Eldar, <a href="/A377563/b377563.txt">Table of n, a(n) for n = 1..10000</a>
%t A377563 f[p_, e_] := 2^DigitCount[e, 2, 1]/(e + 1); q[1] = False; q[n_] := Times @@ f @@@ FactorInteger[n] < 1/2; Select[Range[800], q]
%o A377563 (PARI) is(n) = {my(f = factor(n)); vecprod(apply(x -> (1 << hammingweight(x)) / (x+1), f[, 2])) < 1/2;}
%Y A377563 Cf. A000005, A037445, A062289, A077609, A083329, A158582, A327839, A335832, A348341, A377562.
%K A377563 nonn,easy
%O A377563 1,1
%A A377563 _Amiram Eldar_, Nov 01 2024