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 A274141 #29 Jan 12 2025 04:58:41 %S A274141 4,8,12,16,20,24,25,27,28,32,36,40,44,48,49,50,52,54,56,60,64,68,72, %T A274141 75,76,80,81,84,88,92,96,98,100,104,108,112,116,120,121,124,125,128, %U A274141 132,135,136,140,144,147,148,150,152,156,160,162,164,168,169,172,175,176 %N A274141 Positive numbers divisible by 3^3 or by the square of some other prime. %C A274141 Or numbers n>=4 having a divisor k^2>=4 such that n and n/k^2 equal modulo 3. %C A274141 All positive multiples of 4 are in the sequence. %C A274141 Or numbers n such that there is a smaller positive number j == n (mod 3) such that sqrt(j*n) is an integer. The smallest such j corresponds to the greatest k; or, the same, j = 3*A007913(n/3), if n is divisible by 3 and otherwise j=A007913(n). %C A274141 Or complement to the sequence: S, 3*S and 9*S, where S denotes the sequence of the squarefree numbers not divisible by 3. %H A274141 Amiram Eldar, <a href="/A274141/b274141.txt">Table of n, a(n) for n = 1..10000</a> %F A274141 Let A(x) be the number of a(n)<=x. Then A(x)~(1 - 6.5/Pi^2)*x = 0.34141230...*x as x goes to infinity. %t A274141 Select[Range[200], (e = IntegerExponent[#, 3]) > 2 || ! SquareFreeQ[#/3^e] &] (* _Amiram Eldar_, Feb 25 2021 *) %o A274141 (PARI) isok(n) = (((v=valuation(n, 3)) >= 3) || (((m = n/3^v) > 1) && (vecmax((factor(m))[,2]) >=2))); \\ _Michel Marcus_, Jun 12 2016 %Y A274141 Cf. A046790, A046791, A007913. %K A274141 nonn %O A274141 1,1 %A A274141 _Vladimir Shevelev_, Jun 11 2016