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

1, 4, 9, 12, 16, 18, 20, 25, 28, 36, 44, 45, 48, 49, 50, 52, 60, 63, 64, 68, 75, 76, 80, 81, 84, 90, 92, 98, 99, 100, 112, 116, 117, 121, 124, 126, 132, 140, 144, 147, 148, 150, 153, 156, 162, 164, 169, 171, 172, 175, 176, 180, 188, 192, 196, 198, 204, 207, 208

Offset

1,2

Comments

First differs from A240112 at n = 30.

Numbers k such that A051903(k) is even.

The asymptotic density of this sequence is Sum_{k>=2} (-1)^k * (1 - 1/zeta(k)) = 0.27591672059822700769... .

Links

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

Mathematica

Select[Range[210], # == 1 || EvenQ[Max[FactorInteger[#][[;; , 2]]]] &]

Prog

(PARI) lista(kmax) = for(k = 1, kmax, if(k == 1	|| !(vecmax(factor(k)[, 2])%2), print1(k, ", ")));

Crossrefs

Cf. A051903, A240112.

Subsequences: A000290, A000302, A000583, A001014, A001016, A001025, A008454, A062503, A067259.

Similar sequences: A060476, A074661, A096432, A336064, A368715.

Sequence in context: A162643 A072587 A240112 * A162645 A351575 A348739

Adjacent sequences: A368711 A368712 A368713 * A368715 A368716 A368717

Keyword

nonn,easy

Author

Amiram Eldar, Jan 04 2024

Status

approved