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On the number of prime factors of summands of partitions

Cécile DartygeAndrás SárközyMihály Szalay — 2006

Journal de Théorie des Nombres de Bordeaux

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.

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