cp's OEIS Frontend

A377817 Numbers that have more than one even exponent in their prime factorization.

%I A377817 #11 Nov 09 2024 08:26:44
%S A377817 36,100,144,180,196,225,252,300,324,396,400,441,450,468,484,576,588,
%T A377817 612,676,684,700,720,784,828,882,900,980,1008,1044,1089,1100,1116,
%U A377817 1156,1200,1225,1260,1296,1300,1332,1444,1452,1476,1521,1548,1575,1584,1600,1620,1692,1700,1764,1800
%N A377817 Numbers that have more than one even exponent in their prime factorization.
%C A377817 Subsequence of A072413 and differs from it by not having the terms 216, 1000, 1080, 1512, ... .
%C A377817 Each term can be represented in a unique way as m * k^2, where m is an exponentially odd number (A268335) and k is a composite number that is coprime to m.
%C A377817 Numbers k such that A350388(k) is a square of a composite number (A062312 \ {1}).
%C A377817 The asymptotic density of this sequence is 1 - Product_{p prime} (1 - 1/(p*(p+1))) * (1 + Sum_{p prime} 1/(p^2+p-1)) = 0.032993560887093165933... .
%H A377817 Amiram Eldar, <a href="/A377817/b377817.txt">Table of n, a(n) for n = 1..10000</a>
%t A377817 Select[Range[1800], Count[FactorInteger[#][[;; , 2]], _?EvenQ] > 1 &]
%o A377817 (PARI) is(k) = if(k == 1, 0, my(e = factor(k)[, 2]); #select(x -> !(x%2), e) > 1);
%Y A377817 Complement of the union of A268335 and A377816.
%Y A377817 Subsequence of A072413.
%Y A377817 Cf. A062312, A162645, A350388.
%K A377817 nonn,easy
%O A377817 1,1
%A A377817 _Amiram Eldar_, Nov 09 2024