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 A370787 #12 Mar 02 2024 03:44:36
%S A370787 1,16,64,81,216,256,625,729,864,1000,1024,1296,1944,2401,2744,3375,
%T A370787 3456,4000,4096,5184,6561,7776,9261,10000,10648,10976,11664,13824,
%U A370787 14641,15625,16000,16384,17496,17576,20736,25000,28561,30375,31104,35937,38416,39304,40000
%N A370787 Cubefull numbers with an even number of prime factors (counted with multiplicity).
%C A370787 Jakimczuk (2024) proved:
%C A370787 The number of terms that do not exceed x is N(x) = c * x^(1/3) / 2 + o(x^(1/3)) where c = A362974.
%C A370787 The relative asymptotic density of this sequence within the cubefull numbers is 1/2.
%C A370787 In general, the relative asymptotic density of the s-full numbers (numbers whose exponents in their prime factorization are all >= s) with an even number of prime factors (counted with multiplicity) within the s-full numbers is 1/2 when s is odd.
%H A370787 Amiram Eldar, <a href="/A370787/b370787.txt">Table of n, a(n) for n = 1..10000</a>
%H A370787 Rafael Jakimczuk, <a href="http://dx.doi.org/10.13140/RG.2.2.12174.13124">Arithmetical Functions over the Powerful Part of an Integer</a>, ResearchGate, 2024.
%t A370787 q[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, AllTrue[e, # > 2 &] && OddQ[Total[e]]]; Select[Range[30000], q]
%o A370787 (PARI) is(n) = {my(e = factor(n)[, 2]); n > 1 && vecmin(e) > 2 && vecsum(e)%2;}
%Y A370787 Intersection of A036966 and A028260.
%Y A370787 Complement of A370788 within A036966.
%Y A370787 Subsequence of A370785.
%Y A370787 Cf. A362974.
%K A370787 nonn,easy
%O A370787 1,2
%A A370787 _Amiram Eldar_, Mar 02 2024