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

1,1

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

Mathematica

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

Prog

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

Crossrefs

Cf. A051903.

Subsequence of A013929 and A137257.

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

Sequence in context: A228091 A157849 A137257 * A144976 A119622 A367909

Adjacent sequences: A368712 A368713 A368714 * A368716 A368717 A368718

Keyword

nonn,easy

Author

Amiram Eldar, Jan 04 2024

Status

approved