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 A370788 #11 Mar 02 2024 03:50:59
%S A370788 8,27,32,125,128,243,343,432,512,648,1331,1728,2000,2048,2187,2197,
%T A370788 2592,3125,3888,4913,5000,5488,5832,6859,6912,8000,8192,10125,10368,
%U A370788 12167,15552,16807,16875,19208,19683,20000,21296,21952,23328,24389,27000,27648,27783,29791
%N A370788 Cubefull numbers with an odd number of prime factors (counted with multiplicity).
%C A370788 Jakimczuk (2024) proved:
%C A370788 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 A370788 The relative asymptotic density of this sequence within the cubefull numbers is 1/2.
%C A370788 In general, the relative asymptotic density of the s-full numbers (numbers whose exponents in their prime factorization are all >= s) with an odd number of prime factors (counted with multiplicity) within the s-full numbers is 1/2 when s is odd.
%H A370788 Amiram Eldar, <a href="/A370788/b370788.txt">Table of n, a(n) for n = 1..10000</a>
%H A370788 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 A370788 q[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, AllTrue[e, # > 2 &] && OddQ[Total[e]]]; Select[Range[30000], q]
%o A370788 (PARI) is(n) = {my(e = factor(n)[, 2]); n > 1 && vecmin(e) > 2 && vecsum(e)%2;}
%Y A370788 Intersection of A036966 and A026424.
%Y A370788 Complement of A370787 within A036966.
%Y A370788 Subsequence of A370786.
%Y A370788 Cf. A362974.
%K A370788 nonn,easy
%O A370788 1,1
%A A370788 _Amiram Eldar_, Mar 02 2024