## Problem 618

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bentaylortheonly
Posts: 3
Joined: Wed Jan 17, 2018 7:39 pm

### Problem 618

Why does
S(5)=5+6=11
?
Is that a mistake?

The prime factors of 6 are 2x3 which add up to 5
But why 5? The only prime factors of 5 are 1 and 5 which add up to 6, not 5.
I would have thought S(5) was just 6.
Last edited by RobertStanforth on Sat Jan 20, 2018 9:43 pm, edited 1 time in total.
Reason: Renaming for consistency

traxex
Posts: 77
Joined: Thu Oct 19, 2017 12:30 pm

### Re: PE 618

The number 1 is not a prime. The only prime factor of 5 is itself, which is true for all primes.

Otherwise you would have 5 = 1*5 = 1*1*5 = ..., so the prime factorization would not be unique, which would complicate many definitions.

In the past 1 was often considered a prime. See Wikipedia for a bit of interesting history. Seems like Euler was ahead of his time in this as well.
Technically, everyone is full of himself.

LarryBlake
Posts: 98
Joined: Sat Aug 29, 2009 7:49 pm