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 A375144 #11 Aug 02 2024 03:23:00
%S A375144 36,100,180,196,225,252,300,396,441,450,468,484,588,612,676,684,700,
%T A375144 828,882,980,1044,1089,1100,1116,1156,1225,1260,1300,1332,1444,1452,
%U A375144 1476,1521,1548,1575,1692,1700,1900,1908,1980,2028,2100,2116,2124,2156,2178,2196
%N A375144 Numbers whose prime factorization has exactly two exponents that equal 2 and has no higher exponents.
%C A375144 Numbers of the form m * p^2 * q^2, where p < q are primes, and m is a squarefree number such that gcd(m, p*q) = 1.
%C A375144 Numbers whose powerful part (A057521) is a square of a squarefree semiprime (A085986).
%C A375144 The asymptotic density of this sequence is ((Sum_{p prime} 1/(p*(p+1)))^2 - Sum_{p prime} 1/(p*(p+1))^2)/(2*zeta(2)) = 0.022124574473271163980012... .
%H A375144 Amiram Eldar, <a href="/A375144/b375144.txt">Table of n, a(n) for n = 1..10000</a>
%H A375144 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%e A375144 36 = 2^2 * 3^2 is a term since its prime factorization has exactly two exponents and both are equal to 2.
%t A375144 q[n_] := Module[{e = Sort[FactorInteger[n][[;; , 2]], Greater]}, Length[e] > 1 && e[[1;;2]] == {2, 2} && If[Length[e] > 2, e[[3]] == 1, True]]; Select[Range[2200], q]
%o A375144 (PARI) is(k) = {my(e = vecsort(factor(k)[,2], , 4)~); #e > 1 && e[1..2] == [2,2] && if(#e > 2, e[3] == 1, 1);}
%Y A375144 Cf. A057521, A060687, A085986, A179119.
%Y A375144 Subsequence: A179643.
%K A375144 nonn,easy
%O A375144 1,1
%A A375144 _Amiram Eldar_, Aug 01 2024