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A330244 Weird numbers m (A006037) such that sigma(m)/m > sigma(k)/k for all weird numbers k < m, where sigma(m) is the sum of divisors of m (A000203). 2
70, 10430, 1554070, 5681270, 6365870 (list; graph; refs; listen; history; text; internal format)
Benkoski and Erdős asked whether sigma(n)/n can be arbitrarily large for weird number n. Erdős offered $25 for the solution of this question.
No more terms below 10^10.
Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B2, p. 77.
Stan Benkoski, Are All Weird Numbers Even?, Problem E2308, The American Mathematical Monthly, Vol. 79, No. 7 (1972), p. 774.
S. J. Benkoski and P. Erdős, On weird and pseudoperfect numbers, Mathematics of Computation, Vol. 28, No. 126 (1974), pp. 617-623, alternative link, corrigendum, ibid., Vol. 29, No. 130 (1975), p. 673.
Paul Erdős, Problems and results on combinatorial number theory III, in: M. B. Nathanson (ed.), Number Theory Day, Proceedings of the Conference Held at Rockefeller University, New York 1976, Lecture Notes in Mathematics, Vol 626, Springer, Berlin, Heidelberg, 1977, pp. 43-72. See page 47.
Paul Erdős, Some problems I presented or planned to present in my short talk, in: B. C. Berndt, H. G. Diamond, and A. J. Hildebrand (eds.), Analytic Number Theory, Volume 1, Proceedings of a Conference in Honor of Heini Halberstam, Progress in Mathematics, Vol. 138, Birkhäuser Boston, 1996, pp. 333-335.
The abundancy indices of the terms are sigma(a(n))/a(n) = 2.0571... < 2.0709... < 2.0710... < 2.0716... < 2.0716...
Sequence in context: A213699 A184275 A179713 * A362916 A229776 A362169
Amiram Eldar, Dec 06 2019

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