### Abstract

We discuss in this paper arithmetic properties of the function. Asymptotic estimates of A(n) reveal the connection between A(n) and large prime factors of n. The distribution modulo 2 of A(n) turns out to be an interesting study and congruences involving A(n) are considered. Moreover the very intimate connection between A(n) and the partition of integers into primes provides a natural motivation for its study.

Original language | English |
---|---|

Pages (from-to) | 275-294 |

Number of pages | 20 |

Journal | Pacific Journal of Mathematics |

Volume | 71 |

Issue number | 2 |

Publication status | Published - 1977 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Pacific Journal of Mathematics*,

*71*(2), 275-294.

**On an additive arithmetic function.** / Alladi, K.; Erdős, P.

Research output: Contribution to journal › Article

*Pacific Journal of Mathematics*, vol. 71, no. 2, pp. 275-294.

}

TY - JOUR

T1 - On an additive arithmetic function

AU - Alladi, K.

AU - Erdős, P.

PY - 1977

Y1 - 1977

N2 - We discuss in this paper arithmetic properties of the function. Asymptotic estimates of A(n) reveal the connection between A(n) and large prime factors of n. The distribution modulo 2 of A(n) turns out to be an interesting study and congruences involving A(n) are considered. Moreover the very intimate connection between A(n) and the partition of integers into primes provides a natural motivation for its study.

AB - We discuss in this paper arithmetic properties of the function. Asymptotic estimates of A(n) reveal the connection between A(n) and large prime factors of n. The distribution modulo 2 of A(n) turns out to be an interesting study and congruences involving A(n) are considered. Moreover the very intimate connection between A(n) and the partition of integers into primes provides a natural motivation for its study.

UR - http://www.scopus.com/inward/record.url?scp=84972540664&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972540664&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84972540664

VL - 71

SP - 275

EP - 294

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 2

ER -