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 A096490 #17 Aug 16 2024 21:20:08
%S A096490 60,120,168,180,240,252,300,336,360,420,480,504,540,600,660,672,720,
%T A096490 756,780,792,840,900,924,936,960,1008,1020,1080,1140,1176,1200,1260,
%U A096490 1320,1344,1380,1440,1500,1512,1560,1584,1620,1680,1740,1764,1800,1848,1860
%N A096490 Numbers k such that sigma_2(k) >= (3/2) * k^2, where sigma_2(k) is the sum of the squares of the divisors of k.
%C A096490 From _Amiram Eldar_, Aug 16 2024: (Start)
%C A096490 All the terms are divisible by 6 because sigma_2(k)/k^2 < 3*zeta(2)/4 = 1.2337... < 3/2 for odd numbers k, and sigma_2(k)/k^2 < 8*zeta(2)/9 = 1.462... < 3/2 for numbers k that are not divisible by 3.
%C A096490 There are no 3-smooth numbers (A003586) in this sequence, but for any 5-rough number (A007310) k > 1 there are infinitely many 3-smooth numbers m such that their product k*m is a term.
%C A096490 The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 1, 25, 259, 2578, 25823, 258026, 2580715, 25806329, 258066116, 2580658731, ... . Apparently, the asymptotic density of this sequence exists and equals 0.025806... . (End)
%H A096490 Charles R Greathouse IV, <a href="/A096490/b096490.txt">Table of n, a(n) for n = 1..10000</a>
%F A096490 A001221(a(n)) >= 3. - _Amiram Eldar_, Aug 16 2024
%e A096490 For k = 60: 1 + 4 + 9 + 16 + 25 + 36 + 100 + 144 + 225 + 400 + 900 + 3600 = 5460 > (3/2) * 3600 = 5400.
%t A096490 Do[s=DivisorSigma[2, n]/(n^2); If[Greater[s, 3/2], Print[n]], {n, 1, 10000}]
%t A096490 Select[Range[2000],DivisorSigma[2,#]/#^2>=3/2&] (* _Harvey P. Dale_, Mar 05 2013 *)
%o A096490 (PARI) is(n)=sigma(n,-2) >= 3/2 \\ _Charles R Greathouse IV_, Feb 03 2018
%Y A096490 Cf. A001157, A056866, A118671 (primitive terms).
%Y A096490 Cf. A001221, A003586, A007310, A013661.
%K A096490 nonn,easy
%O A096490 1,1
%A A096490 _Labos Elemer_, Jun 25 2004
%E A096490 Name corrected by _Charles R Greathouse IV_, Feb 03 2018