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    Weingartner, A. 2015. PRACTICAL NUMBERS AND THE DISTRIBUTION OF DIVISORS. The Quarterly Journal of Mathematics, Vol. 66, Issue. 2, p. 743.


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  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society, Volume 27, Issue 3
  • May 1979, pp. 319-331

Some problems in partitio numerorum

  • P. Erdös (a1) and J. H. Loxton (a2)
  • DOI: http://dx.doi.org/10.1017/S144678870001243X
  • Published online: 01 April 2009
Abstract
Abstract

We consider some unconventional partition problems in which the parts of the partition are restricted by divisibility conditions, for example, partitions n = a1+…+ak into positive integers a1, …, ak such that a1 ∣ a2 ∣ … ∣ ak. Some rather weak estimates for the various partition functions are obtained.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

P. Erdös (1941), ‘On some asymptotic formulas in the theory of “factorisatio numerorum”’, Annals of Math. 42, 989993.

E. Grosswald (1974), ‘Verallgemeinerte Eulersche Zahlen’, Math. Z. 140, 173177.

A. E. Ingham (1941), ‘A Tauberian theorem for partitions’, Ann. of Math. 42, 10751090.

W. B. Pennington (1953), ‘On Mahler's partition problem’, Ann. of Math. 57, 531546.

W. Sierpinski (1955), ‘Sur une propriété des nombres naturels’, Annali di Mat. pura ed appl. (4) 39, 6974.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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