On the number of prime factors of summands of partitions

Cécile Dartyge (1) , Andras Sarkozy (2) , Mihaly Szalay (2)

1 IECN - Institut Élie Cartan de Nancy
2 Alfred Renyi Mathematical Institute

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.

Mots clés: partitions; prime factors

Domaines: Théorie des nombres [math.NT]

Cécile Dartyge, Andras Sarkozy, Mihaly Szalay. On the number of prime factors of summands of partitions. Journal de Théorie des Nombres de Bordeaux, 2006, 18 (1), pp.73-87. ⟨hal-00091876⟩