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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.

A381313 Numbers that are divisible by the cube of an odd prime.

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%I A381313 #8 Feb 21 2025 08:13:27
%S A381313 27,54,81,108,125,135,162,189,216,243,250,270,297,324,343,351,375,378,
%T A381313 405,432,459,486,500,513,540,567,594,621,625,648,675,686,702,729,750,
%U A381313 756,783,810,837,864,875,891,918,945,972,999,1000,1026,1029,1053,1080,1107,1125
%N A381313 Numbers that are divisible by the cube of an odd prime.
%C A381313 Numbers whose odd part is not cubefree.
%C A381313 The asymptotic density of this sequence is 1 - 8/(7*zeta(3)) = 1 - 1/A233091 = 0.04924871705062003579... .
%H A381313 Amiram Eldar, <a href="/A381313/b381313.txt">Table of n, a(n) for n = 1..10000</a>
%t A381313 cubeFreeQ[k_] := Max[FactorInteger[k][[;;, 2]]] < 3; q[k_] := !cubeFreeQ[k / 2^IntegerExponent[k, 2]]; Select[Range[1200], q]
%o A381313 (PARI) iscubefree(k) = if(k == 1, 1, vecmax(factor(k)[, 2]) < 3);
%o A381313 isok(k) = !iscubefree(k >> valuation(k, 2));
%Y A381313 Subsequence of A046099 and A038838.
%Y A381313 Cf. A000265, A002117, A233091.
%K A381313 nonn,easy
%O A381313 1,1
%A A381313 _Amiram Eldar_, Feb 19 2025