ON VALUES OF d(n!)/m!, ϕ(n!)/m! AND σ(n!)/m!
2010 ◽
Vol 06
(06)
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pp. 1199-1214
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For f one of the classical arithmetic functions d, ϕ and σ, we establish constraints on the quadruples (n, m, a, b) of integers satisfying f(n!)/m! = a/b. In particular, our results imply that as nm tends to infinity, the number of distinct prime divisors dividing the product of the numerator and denominator of the fraction f(n!)/m!, when reduced, tends to infinity.
1966 ◽
Vol 9
(4)
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pp. 427-431
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1967 ◽
Vol 10
(1)
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pp. 65-73
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1950 ◽
Vol 3
(3)
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pp. 259-272
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Keyword(s):
2014 ◽
Vol 150
(10)
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pp. 1729-1741
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