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

36, 100, 144, 180, 196, 225, 252, 300, 324, 396, 400, 441, 450, 468, 484, 576, 588, 612, 676, 684, 700, 720, 784, 828, 882, 900, 980, 1008, 1044, 1089, 1100, 1116, 1156, 1200, 1225, 1260, 1296, 1300, 1332, 1444, 1452, 1476, 1521, 1548, 1575, 1584, 1600, 1620, 1692, 1700, 1764, 1800

Offset

1,1

Comments

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

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.

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

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... .

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

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

Prog

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

Crossrefs

Complement of the union of A268335 and A377816.

Subsequence of A072413.

Cf. A062312, A162645, A350388.

Sequence in context: A137945 A250812 A072413 * A131605 A376119 A296204

Adjacent sequences: A377814 A377815 A377816 * A377818 A377819 A377820

Keyword

nonn,easy

Author

Amiram Eldar, Nov 09 2024

Status

approved