A368715 Numbers that are not coprime to the maximal exponent in their prime factorization.

4, 12, 16, 18, 20, 24, 27, 28, 36, 44, 48, 50, 52, 54, 60, 64, 68, 72, 76, 80, 84, 90, 92, 98, 100, 108, 112, 116, 120, 124, 126, 132, 135, 140, 144, 148, 150, 156, 160, 162, 164, 168, 172, 176, 180, 188, 189, 192, 196, 198, 204, 208, 212, 216, 220, 228, 234, 236, 240, 242, 244

Offset: 1

Author

Amiram Eldar, Jan 04 2024

Keywords

• nonn
• easy

Comments

Subsequence of A137257 and first differs from it at n = 51.

Numbers k such that gcd(k, A051903(k)) > 1.

Includes all the nonsquarefree terms of A336064.

The asymptotic density of this sequence is 1 - 1/zeta(2) - Sum_{k>=2} (1/(f(k+1, k) * zeta(k+1)) - 1/(f(k, k) * zeta(k))) = 0.24998449199080279703..., where f(e, m) = Product_{primes p|m} ((1-1/p^e)/(1-1/p)).

Links

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

Crossrefs

Cf. A051903.

Subsequence of A013929 and A137257.

Similar sequences: A060476, A074661, A096432, A336064, A368714.

Programs

Mathematica

Select[Range[210], !CoprimeQ[#, Max[FactorInteger[#][[;;, 2]]]] &]

PARI

lista(kmax) = for(k = 2, kmax, if(gcd(k, vecmax(factor(k)[,2])) > 1, print1(k, ", ")));