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historical prime factor, hpf(n): is defined as the prime factor of $n$ that has not appeared for the longest time in ${hpf(1),..., hpf(n-2),hpf(n-1)}$. hpf(1)=1

hpf(n) selects the most recently unoccurring prime factor of $n$. For example,

hpf(6)=3, because hpf(4)=2;hpf(12)=2, because hpf(9)=3, hpf(8)=2, here 2 is more historical than 3;
hpf(30)=2, because recently hpf(27)=3, hpf(25)=5.

Note: hpf(120)=hpf(125)=5, 113..127