List of recreational number theory topics

Number sequences

• Integer sequence
• Fibonacci sequence
• *Golden mean base
• *Fibonacci coding
• Lucas sequence
• Padovan sequence
• Figurate numbers
• *Polygonal number
• **Triangular number
• **Square number
• **Pentagonal number
• **Hexagonal number
• **Heptagonal number
• **Octagonal number
• **Nonagonal number
• **Decagonal number
• *Centered polygonal number
• **Centered square number
• **Centered pentagonal number
• **Centered hexagonal number
• *Tetrahedral number
• *Pyramidal number
• **Triangular pyramidal number
• **Square pyramidal number
• **Pentagonal pyramidal number
• **Hexagonal pyramidal number
• **Heptagonal pyramidal number
• *Octahedral number
• *Star number
• Perfect number
• *Quasiperfect number
• *Almost perfect number
• *Multiply perfect number
• *Hyperperfect number
• *Semiperfect number
• *Primitive semiperfect number
• *Unitary perfect number
• *Weird number
• Untouchable number
• Amicable number
• Sociable number
• Abundant number
• Deficient number
• Amenable number
• Aliquot sequence
• Super-Poulet number
• Lucky number
• Powerful number
• Primeval number
• Palindromic number
• Triangular square number
• Harmonic divisor number
• Sphenic number
• Smith number
• Double Mersenne number
• Zeisel number
• Heteromecic number
• Niven numbers
• Superparticular number
• Highly composite number
• Highly totient number
• Practical number
• Juggler sequence
• Look-and-say sequence

  Digits

• Polydivisible number
• Automorphic number
• Armstrong number
• Self number
• Harshad number
• Keith number
• Kaprekar number
• Digit sum
• Persistence of a number
• Perfect digital invariant
• *Happy number
• Perfect digit-to-digit invariant
• Factorion
• Emirp
• Palindromic prime
• Home prime
• Normal number
• *Stoneham number
• *Champernowne constant
• *Absolutely normal number
• Repunit
• Repdigit

  Prime and related sequences

• Semiprime
• Almost prime
• Unique prime
• Factorial prime
• Permutable prime
• Palindromic prime
• Cuban prime
• Lucky prime

  Magic squares, etc.

• Ulam spiral
• Magic star
• Magic square
• *Frénicle standard form
• *Prime reciprocal magic square
• *Trimagic square
• *Multimagic square
• *Panmagic square
• *Satanic square
• *Most-perfect magic square
• *Geometric magic square
• *Conway's Lux method for magic squares
• Magic cube
• *Perfect magic cube
• *Semiperfect magic cube
• *Bimagic cube
• *Trimagic cube
• *Multimagic cube
• Magic hypercube
• Magic constant
• Squaring the square