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## Number Theory: A Math Puzzle That Uses No Math

A cache by _Wynn Message this owner
Hidden : 7/6/2018
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### Geocache Description:

The geocache is not at the posted coordinates*. To get the actual location, you must solve the puzzle below and enter the two-word solution into the certitude checker below.

Number theory is not as scary as it sounds, and neither is this puzzle! Formerly known as the grade school subject arithmetic, it is a branch of mathematics that deals solely with integers. It seems that mathematicians really like coming up with number sequences and giving them names. I mean, really... I had no idea. Honestly, given how many of them have been defined, it's like anybody can do it. Anybody can do this puzzle too. It doesn't require any math, other than the ability to count. After solving this, I have a feeling you'll be seeing numbers and patterns everywhere...

Identify the numbers described below. All sequences used in this puzzle are in base 10, which is our normal numbering system.

 1st perfect number 2nd perfect totient number 3rd semiperfect number 5th happy number 1st primitive abundant number 2nd superior highly composite number 7th Perrin number 1st emirp 1st highly totient number 1st sublime number 1st Wilson prime 5th standard Ulam number 8th deficient number 3rd Mersenne prime 3rd pentagonal number 1st composite number 3rd centered hexagonal number 4th Fubini number 2nd untouchable number 2nd highly cototient number 2nd Fibonacci number 3rd sparsely totient number 2nd Kaprekar number 1st centered triangular prime 4th tetrahedral number

You can validate your puzzle solution with certitude.

*Not part of the puzzle: The posted coordinates are the intersection of 163rd PL SE and SE 66th ST. 163 is the 9th and final Heegner number, and 66 is the 3rd sphenic number. Isn't that fascinating? No, I suppose it isn't.

Pnpur: N uvag vf cebivqrq va gur fbyhgvba purpxre

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)

Find...

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