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

Author

Amiram Eldar, Jan 04 2024

Keywords

• nonn
• easy

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

Crossrefs

Cf. A051903, A240112.

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

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

Programs

Mathematica

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

PARI

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