data/problems/362.yml
---
:id: 362
:name: Squarefree factors
:url: https://projecteuler.net/problem=362
:content: "Consider the number 54. \n54 can be factored in 7 distinct ways into one
or more factors larger than 1: \n54, 2×27, 3×18, 6×9, 3×3×6, 2×3×9 and 2×3×3×3.
\ \nIf we require that the factors are all squarefree only two ways remain: 3×3×6
and 2×3×3×3.\n\nLet's call Fsf(<var>n</var>) the number of ways <var>n</var> can
be factored into one or more squarefree factors larger than 1, so Fsf(54)=2.\n\nLet
S(<var>n</var>) be ∑Fsf(<var>k</var>) for <var>k</var>=2 to <var>n</var>.\n\nS(100)=193.\n\nFind
S(10 000 000 000).\n\n"