Definitions

Prime
Chen Prime
Emirp Prime
Good Prime
Honaker Prime
Mersenne Prime
Ormiston Prime
Pierpont Prime
Sophie Germain Prime
Twin Prime
MECE(
Strong Prime
Balanced Prime
Weak Prime
)
Composite
Semi Prime
⊃Brilliant
Sphenic
Interprime
MECE(
Economical
Wasteful
) Economical =
Frugal
∪
Equidigital
Deceptive
Droll
Duffinian
Enlightened
Gapful
Highly Composite
Hoax
Joke
Jordan-Polya
O'Halloran
Perfect Power
Poulet
Practical
Ruth-Aaron
Unprimeable

Powerful
⊃Achilles
MECE(
Abundant
Perfect
Deficient
) Abundant ⊃ (
Admirable
Super Abundant
Weird
)
Anti-Perfect
Semiperfect
Zumkeller
MECE(
Evil
Odious
)
Pernicious
Amenable
Amicable
Astonishing
Automorphic
Betrothed
Congruent
Cullen
Curzon
Cyclic
Cyclic (group theory)
Square-Free
D-Number
de Polignac
Digitally Powerful
Esthetic
Eulerian
Factorial
Friedman
Happy
Highly Totient
Hogben
Idoneal
Impolite
Inconsummate
Junction
Self
Kaprekar
Leyland
Lonely
Lucky
Magic
Magnanimous
Modest
Padovan
Partition
Primeval
Proth
Sastry
Untouchable
Vampire

Niven
⊃ (
Super Niven
Moran
)
Nude
⊃ (
Lynch-Bell
Zuckerman
)
Katadrome
Metadrome
Palindrome
Straight Line
Combinatorial sequences:
Bell
Cake
Catalan
Pancake
Generated from recurrences:
Fibonacci
Keith
Jacobsthal
Lucas
Gilda
Motzkin
Perrin
Ulam
Figurative sequences:
Triangular
Square
Star
Cube
Pronic
Toothpick

And Or     Refresh