Wolstenholme number

Short description: Number that is the numerator of the generalized harmonic number H_(n,2)

Not to be confused with Wolstenholme prime.

In mathematics, a Wolstenholme number is a number that is the numerator of the generalized harmonic number Hn,2.

The first such numbers are 1, 5, 49, 205, 5269, 5369, 266681, 1077749, ... (sequence A007406 in the OEIS).

These numbers are named after Joseph Wolstenholme, who proved Wolstenholme's theorem on modular relations of the generalized harmonic numbers.

## References

* Weisstein, Eric W.. "WolstenholmeNumber". http://mathworld.wolfram.com/WolstenholmeNumber.html.

* v
* t
* e

Classes of natural numbers

Powers and
related numbers|

* Achilles
* Power of 2
* Power of 10
* Square
* Cube
* Fourth power
* Fifth power
* Sixth power
* Seventh power
* Perfect power
* Powerful
* Prime power

Of the form
a × 2b ± 1|

* Cullen
* Double Mersenne
* Fermat
* Mersenne
* Proth
* Thabit
* Woodall

Other polynomial
numbers|

* Carol
* Hilbert
* Idoneal
* Kynea
* Leyland
* Loeschian
* Lucky numbers of Euler

Recursively defined
numbers|

* Fibonacci
* Jacobsthal
* Leonardo
* Lucas
* Padovan
* Pell
* Perrin

Possessing a
specific set
of other numbers|

* Knödel
* Riesel
* Sierpinski

Expressible via
specific sums|

* Nonhypotenuse
* Polite
* Practical
* Primary pseudoperfect
* Ulam
* Wolstenholme

Figurate numbers|

| 2-dimensional|

| centered|

* Centered triangular
* Centered square
* Centered pentagonal
* Centered hexagonal
* Centered heptagonal
* Centered octagonal
* Centered nonagonal
* Centered decagonal
* Star

|

non-centered|

* Triangular
* Square
* Square triangular
* Pentagonal
* Hexagonal
* Heptagonal
* Octagonal
* Nonagonal
* Decagonal
* Dodecagonal

3-dimensional|

| centered|

* Centered tetrahedral
* Centered cube
* Centered octahedral
* Centered dodecahedral
* Centered icosahedral

|

non-centered|

* Tetrahedral
* Cube
* Octahedral
* Dodecahedral
* Icosahedral
* Stella octangula

pyramidal|

* Square pyramidal
* Pentagonal pyramidal
* Hexagonal pyramidal
* Heptagonal pyramidal

4-dimensional|

| centered|

* Centered pentachoric
* Squared triangular

|

non-centered|

* Pentatope
* 4-cube

Base-dependent
numbers|

| Arithmetic functions and dynamics|

* Digit sum
* Digital root
* Multiplicative
* Dudeney
* Factorion
* Happy
* Kaprekar
* Kaprekar's constant
* Keith
* Lychrel
* Meertens
* Narcissistic
* Perfect digit-to-digit invariant
* Perfect digital invariant
* Persistence
* Additive
* Multiplicative
* Self
* Sum-product

|

P-adic numbers related|

* Automorphic

Divisor related|

* Equidigital
* Extravagant
* Frugal
* Harshad
* Polydivisible
* Smith

Digit-composition related|

* Palindromic
* Pandigital
* Repdigit
* Repunit
* Self-descriptive
* Smarandache–Wellin
* Strictly non-palindromic
* Undulating

Digit-permutation related|

* Cyclic
* Digit-reassembly
* Parasitic
* Primeval
* Transposable

Other|

* Friedman
* Vampire

Combinatorial
numbers|

* Bell
* Cake
* Catalan
* Dedekind
* Delannoy
* Euler
* Fuss–Catalan
* Lazy caterer's sequence
* Lobb
* Motzkin
* Narayana
* Ordered Bell
* Schröder
* Schröder–Hipparchus

Pseudoprimes|

* Carmichael number
* Catalan pseudoprime
* Elliptic pseudoprime
* Euler pseudoprime
* Euler–Jacobi pseudoprime
* Fermat pseudoprime
* Frobenius pseudoprime
* Lucas pseudoprime
* Somer–Lucas pseudoprime
* Strong pseudoprime

Arithmetic functions|

| By properties of σ(n)|

* Abundant
* Arithmetic
* Colossally abundant
* Descartes
* Hemiperfect
* Highly abundant
* Highly composite
* Hyperperfect
* Multiply perfect
* Perfect
* Practical number
* Primitive abundant
* Quasiperfect
* Refactorable
* Sublime
* Superabundant
* Superior highly composite
* Superperfect
* Untouchable

|

By properties of Ω(n)|

* Almost prime
* Semiprime

By properties of φ(n)|

* Highly cototient
* Highly totient
* Noncototient
* Nontotient
* Perfect totient
* Sparsely totient

By properties of s(n)|

* Almost perfect
* Amicable
* Betrothed
* Deficient
* Perfect
* Semiperfect
* Sociable

Other|

* Euclid
* Fortunate

Dividing a quotient|

* Wieferich
* Wall–Sun–Sun
* Wolstenholme prime
* Wilson

Other prime factor
or divisor related
numbers|

* Blum
* Erdős–Nicolas
* Erdős–Woods
* Friendly
* Giuga
* Harmonic divisor
* Lucas–Carmichael
* Pronic
* Regular
* Rough
* Smooth
* Sociable
* Sphenic
* Størmer
* Super-Poulet
* Zeisel

Binary numbers|

* Evil
* Odious
* Pernicious

Generated
via a sieve|

* Lucky
* Prime

Sorting related|

* Pancake number
* Sorting number

Natural language related|

* Aronson's sequence
* Ban

Graphemics related|

* Strobogrammatic

* Mathematics portal

0.00

(0 votes)

Original source: https://en.wikipedia.org/wiki/Wolstenholme number. Read more

|

Retrieved from "https://handwiki.org/wiki/index.php?title=Wolstenholme_number&oldid=3977073"
*[v]: View this template
*[t]: Discuss this template
*[e]: Edit this template