On the number of prime factors of summands of partitions
Journal de théorie des nombres de Bordeaux, Volume 18 (2006) no. 1, pp. 73-87.

We present various results on the number of prime factors of the parts of a partition of an integer. We study the parity of this number, the extremal orders and we prove a Hardy-Ramanujan type theorem. These results show that for almost all partitions of an integer the sequence of the parts satisfies similar arithmetic properties as the sequence of natural numbers.

Nous présentons plusieurs résultats sur le nombre de facteurs premiers des parts d’une partition d’un entier. Nous étudions la parité, les ordres extrémaux et nous démontrons un théorème analogue au théorème de Hardy-Ramanujan. Ces résultats montrent que pour presque toutes les partitions d’un entier, la suite des parts vérifie des propriétés arithmétiques similaires à la suite des entiers naturels.

DOI: 10.5802/jtnb.534
Dartyge, Cécile 1; Sárközy, András 2; Szalay, Mihály 2

1 Institut Élie Cartan Université Henri Poincaré–Nancy 1 BP 239 54506 Vandœuvre Cedex, France
2 Department of Algebra and Number Theory Eötvös Loránd University H-1117 Budapest Pázmány Péter sétány 1/C, Hungary
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Dartyge, Cécile; Sárközy, András; Szalay, Mihály. On the number of prime factors of summands of partitions. Journal de théorie des nombres de Bordeaux, Volume 18 (2006) no. 1, pp. 73-87. doi : 10.5802/jtnb.534. http://www.numdam.org/articles/10.5802/jtnb.534/

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