MathDB
2014-2015 Spring OMO #30

Source:

April 14, 2015
Online Math Open

Problem Statement

Let SS be the value of ∑n=1∞d(n)+∑m=1ν2(n)(m−3)d(n2m)n,\sum_{n=1}^\infty \frac{d(n) + \sum_{m=1}^{\nu_2(n)}(m-3)d\left(\frac{n}{2^m}\right)}{n}, where d(n)d(n) is the number of divisors of nn and ν2(n)\nu_2(n) is the exponent of 22 in the prime factorization of nn. If SS can be expressed as (ln⁡m)n(\ln m)^n for positive integers mm and nn, find 1000n+m1000n + m.
Proposed by Robin Park
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