A374587 The maximum exponent in the prime factorization of the numbers that are not coprime to the maximum exponent in their prime factorization.

2, 2, 4, 2, 2, 3, 3, 2, 2, 2, 4, 2, 2, 3, 2, 6, 2, 3, 2, 4, 2, 2, 2, 2, 2, 3, 4, 2, 3, 2, 2, 2, 3, 2, 4, 2, 2, 2, 5, 4, 2, 3, 2, 4, 2, 2, 3, 6, 2, 2, 2, 4, 2, 3, 2, 2, 2, 2, 4, 2, 2, 2, 8, 2, 3, 2, 3, 4, 2, 2, 2, 2, 3, 2, 4, 2, 2, 3, 2, 6, 4, 2, 4, 2, 2, 2, 2

Offset

1,1

Links

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

Formula

a(n) = A051903(A368715(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=2} k * d(k) / Sum_{k>=2} d(k) = 2.74240523513766773312..., where d(k) = (1 - 1/f(k+1, k))/zeta(k+1) - (1 - 1/f(k, k))/zeta(k), and f(e, m) = Product_{primes p|m} ((1-1/p^e)/(1-1/p)).

Mathematica

f[n_] := Module[{e = If[n == 1, 0, Max[FactorInteger[n][[;; , 2]]]]}, If[!CoprimeQ[n, e], e, Nothing]]; Array[f, 350]

Prog

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

Crossrefs

Cf. A051903, A368715, A374586.

Sequence in context: A328400 A239676 A295639 * A182982 A090047 A245525

Adjacent sequences: A374584 A374585 A374586 * A374588 A374589 A374590

Keyword

nonn,easy

Author

Amiram Eldar, Jul 12 2024

Status

approved