FactorInteger

Notations

Traditional name

Traditional notation

Mathematica StandardForm notation

Primary definition

Specific values

Specialized values

Values at fixed points

General characteristics

Domain and analyticity

factors(n) is a nonanalytical function which is defined only for integer n.

Symmetries and periodicities

Symmetry

No symmetry

Periodicity

No periodicity

Identities

Functional identities

Operations

Limit operation

Summation

Asymptotic finite summation

Representations through equivalent functions

With related functions

Theorems

Fundamental theorem of arithmetic

Every possible integer n can be uniquely decomposed into the form

n==(∏_(k=1)^r)((Subscript[p, k])^(Subscript[n, k])),(Subscript[p, k])∈ℙ∧(Subscript[n, k])∈(SuperPlus[ℕ]),(Subscript[p, k])<(Subscript[p, k+1]).

History

– G. H. Hardy, S. Ramanujan (1917)

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