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Find the smallest odd amusing integer

Source: Baltic Way 2010

November 19, 2010
modular arithmeticnumber theory proposednumber theory

Problem Statement

For a positive integer kk, let d(k)d(k) denote the number of divisors of kk and let s(k)s(k) denote the digit sum of kk. A positive integer nn is said to be amusing if there exists a positive integer kk such that d(k)=s(k)=nd(k)=s(k)=n. What is the smallest amusing odd integer greater than 11?
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