A377817 - OEIS

%I #11 Nov 09 2024 08:26:44

%S 36,100,144,180,196,225,252,300,324,396,400,441,450,468,484,576,588,

%T 612,676,684,700,720,784,828,882,900,980,1008,1044,1089,1100,1116,

%U 1156,1200,1225,1260,1296,1300,1332,1444,1452,1476,1521,1548,1575,1584,1600,1620,1692,1700,1764,1800

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

%C Subsequence of A072413 and differs from it by not having the terms 216, 1000, 1080, 1512, ... .

%C 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 Numbers k such that A350388(k) is a square of a composite number (A062312 \ {1}).

%C 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 Amiram Eldar, <a href="/A377817/b377817.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Range[1800], Count[FactorInteger[#][[;; , 2]], _?EvenQ] > 1 &]

%o (PARI) is(k) = if(k == 1, 0, my(e = factor(k)[, 2]); #select(x -> !(x%2), e) > 1);

%Y Complement of the union of A268335 and A377816.

%Y Subsequence of A072413.

%Y Cf. A062312, A162645, A350388.

%K nonn,easy

%O 1,1

%A _Amiram Eldar_, Nov 09 2024