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# 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 or , to avoid ambiguities given that or include 0 for many authors^{[1]} (which is sometimes denoted by ,^{[2]} by others)^{[3]}.

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 (little omega(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) (big Omega(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**)

## Notes

- ↑ For example, Steven J. Miller & Ramin Takloo-Bighash,
*An Invitation to Modern Number Theory*, (2006) Princeton and Oxford: Princeton University Press, p. xix. - ↑ Eberhard Freitag & Rolf Busam,
*Complex Analysis*, 2nd Ed. (2009) Springer-Verlag (Universitext), pp. 519-520. - ↑ Wikipedia, Natural number, http://en.wikipedia.org/wiki/Natural_number