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Cécile Dartyge; András Sárközy; Mihály Szalay
On the number of prime factors of summands of partitions
Journal de théorie des nombres de Bordeaux, 18 no. 1 (2006), p. 73-87, doi: 10.5802/jtnb.534
Article PDF | Reviews MR 2245876 | Zbl 1108.11078

Résumé - Abstract

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.

Bibliography

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