

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




OFFSET

1,1


COMMENTS

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.


REFERENCES

Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B2, p. 77.


LINKS

S. J. Benkoski and P. Erdős, On weird and pseudoperfect numbers, Mathematics of Computation, Vol. 28, No. 126 (1974), pp. 617623, 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. 4372. 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. 333335.


EXAMPLE

The abundancy indices of the terms are sigma(a(n))/a(n) = 2.0571... < 2.0709... < 2.0710... < 2.0716... < 2.0716...


CROSSREFS



KEYWORD

nonn,more


AUTHOR



STATUS

approved



