Positive integers

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The positive integers (also called the counting numbers or the whole numbers) are most often what the set of natural numbers refers to, but not always. (Many authors consider zero to be a natural number, although it was not even a number for the ancient Greeks!) The set of all positive integers (or natural numbers) may be denoted

ℕ ⁎

or

ℤ ⁎ +

, to avoid ambiguities given that

ℕ

,

ℤ  +

or

ℤ +

include 0 for many authors (which is sometimes denoted by

ℕ  0

,

ℤ + 0

by others).

A000042 Unary (so to speak, base “1”) representation of natural numbers. (Tally mark representation of natural numbers, where 1 stands for a tally mark.)

{1, 11, 111, 1111, 11111, 111111, 1111111, 11111111, 111111111, 1111111111, 11111111111, 111111111111, 1111111111111, 11111111111111, 111111111111111, 1111111111111111, 11111111111111111, ...}

A000027 Denary (base 10) representation of natural numbers. Also called the whole numbers, the counting numbers or the positive integers.

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, ...}

See also

• Prime factors of n (without multiplicity)  (distinct prime factors of n)
• Number of distinct prime factors of n  (ω (n))
• Sum of distinct prime factors of n  (sodpf (n))
• Product of distinct prime factors of n  (radical of n, rad (n), squarefree kernel of n)

• Prime factors of n (with multiplicity)
• Number of prime factors of n (with multiplicity)  (Ω (n))
• Sum of prime factors of n (with multiplicity)  (sopf (n), integer log of n)
• Product of prime factors of n (with multiplicity)  (positive integers)