A375039 The maximum exponent in the prime factorization of 2*n-1.

0, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1

Offset: 1

Author

Amiram Eldar, Jul 28 2024

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from exponents in factorization of n.

Crossrefs

Bisection of A051903.

Cf. A033150, A375040.

Programs

Mathematica

a[n_] := Max[FactorInteger[2*n - 1][[;; , 2]]]; a[1] = 0; Array[a, 100]

PARI

a(n) = if(n == 1, 0, vecmax(factor(2*n-1)[,2]));

Formula

a(n) = A051903(2*n-1).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 + Sum_{k>=2} (1 - 1/((1-1/2^k) * zeta(k))) = 1.25979668632898014495... .