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# Positive integers

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(Redirected from Counting numbers)

ℕ ⁎ |

ℤ ⁎ + |

ℕ |

ℤ + |

ℤ + |

^{[1]}(which is sometimes denoted by

ℕ 0 |

^{[2]}

ℤ + 0 |

^{[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*(*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)

## 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. - ↑ Natural number—Wikipedia.org.