cp's OEIS Frontend

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.

A368714 Numbers whose maximal exponent in their prime factorization is even.

This page as a plain text file.
%I A368714 #12 Sep 08 2024 17:11:17
%S A368714 1,4,9,12,16,18,20,25,28,36,44,45,48,49,50,52,60,63,64,68,75,76,80,81,
%T A368714 84,90,92,98,99,100,112,116,117,121,124,126,132,140,144,147,148,150,
%U A368714 153,156,162,164,169,171,172,175,176,180,188,192,196,198,204,207,208
%N A368714 Numbers whose maximal exponent in their prime factorization is even.
%C A368714 First differs from A240112 at n = 30.
%C A368714 Numbers k such that A051903(k) is even.
%C A368714 The asymptotic density of this sequence is Sum_{k>=2} (-1)^k * (1 - 1/zeta(k)) = 0.27591672059822700769... .
%H A368714 Amiram Eldar, <a href="/A368714/b368714.txt">Table of n, a(n) for n = 1..10000</a>
%t A368714 Select[Range[210], # == 1 || EvenQ[Max[FactorInteger[#][[;;, 2]]]] &]
%o A368714 (PARI) lista(kmax) = for(k = 1, kmax, if(k == 1 || !(vecmax(factor(k)[,2])%2), print1(k, ", ")));
%Y A368714 Cf. A051903, A240112.
%Y A368714 Subsequences: A000290, A000302, A000583, A001014, A001016, A001025, A008454, A062503, A067259.
%Y A368714 Similar sequences: A060476, A074661, A096432, A336064, A368715.
%K A368714 nonn,easy
%O A368714 1,2
%A A368714 _Amiram Eldar_, Jan 04 2024