MathDB
f(n) = (p_1-1)^{k_1+1}(p_2-1)^{k_2+1}...(pt-1)^{k_t+1}

Source: 2020 Dürer Math Competition Finals Day2 E+15 https://artofproblemsolving.com/community/c1622639_2020_

January 7, 2022
number theory

Problem Statement

The function ff is defined on positive integers : if nn has prime factorization p1k1p2k2...ptktp^{k_1}_{1} p^{k_2}_{2} ...p^{k_t}_{t} then f(n)=(p1−1)k1+1(p2−1)k2+1...(pt−1)kt+1f(n) = (p_1-1)^{k_1+1}(p_2-1)^{k_2+1}...(p_t-1)^{k_t+1}. If we keep using this function repeatedly, starting from any positive integer nn, we will always get to 11 after some number of steps. What is the smallest integer nn for which we need exactly 66 steps to get to 11?
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