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 A362148 #61 Dec 06 2024 13:17:55
%S A362148 24,40,48,54,56,72,80,88,96,104,108,112,120,135,136,144,152,160,162,
%T A362148 168,176,184,189,192,200,208,224,232,240,248,250,264,270,272,280,288,
%U A362148 296,297,304,312,320,324,328,336,344,351,352,360,368,375,376,378,384,392,400
%N A362148 Numbers that are neither cubefree nor cubefull.
%C A362148 In fact, every cubefull number > 1 is noncubefree, but the converse is false.
%C A362148 This sequence = A046099 \ A036966 and lists these counterexamples.
%C A362148 Numbers k such that for some primes p and q, k is divisible by p^3*q but not by q^3. - _Robert Israel_, Apr 28 2023
%C A362148 The asymptotic density of this sequence is 1 - 1/zeta(3) = 0.168092... - _Charles R Greathouse IV_, Apr 28 2023
%C A362148 From _Amiram Eldar_, Sep 17 2023: (Start)
%C A362148 Numbers k such that A360539(k) > 1 and A360540(k) > 1.
%C A362148 Equivalently, numbers that have in their prime factorization at least one exponent that is smaller than 3 and at least one exponent that is larger than 2. (End)
%H A362148 Michael De Vlieger, <a href="/A362148/b362148.txt">Table of n, a(n) for n = 1..10000</a>
%F A362148 Equals A362147 \ A004709.
%F A362148 Sum_{n>=1} 1/a(n) = 1 + zeta(s) - zeta(s)/zeta(3*s) - Product_{p prime}(1 + 1/(p^(2*s)*(p^s-1))), s > 1. - _Amiram Eldar_, Sep 17 2023
%e A362148 24 = 2^3 * 3 is noncubefree as it is divisible by the cube 2^3, but it is not cubefull because 3 divides 24 but 3^3 does not divide 24, hence 24 is a term.
%e A362148 648 = 2^4 * 3^3 is noncubefree as it is divisible by the cube 3^3, but it is also cubefull because primes 2 and 3 divide 648, and 2^3 and 3^3 divide also 648, so 648 is not a term.
%p A362148 filter:= proc(n) local F;
%p A362148 F:= ifactors(n)[2][..,2];
%p A362148 min(F) < 3 and max(F) >= 3
%p A362148 end proc:
%p A362148 select(filter, [$1..400]); # _Robert Israel_, Apr 28 2023
%t A362148 Select[Range[500], Min[(e = FactorInteger[#][[;; , 2]])] < 3 && Max[e] > 2 &] (* _Amiram Eldar_, Apr 09 2023 *)
%o A362148 (PARI) isok(k) = (k>1) && (vecmax(factor(k)[, 2])>2) && (vecmin(factor(k)[, 2])<=2); \\ _Michel Marcus_, Apr 19 2023
%Y A362148 Intersection of A046099 (not cubefree) and A362147 (not cubefull)
%Y A362148 Cf. A004709 (cubefree), A036966 (cubefull), A360539, A360540.
%K A362148 nonn,easy
%O A362148 1,1
%A A362148 _Bernard Schott_, Apr 09 2023