On Representations as a Sum of Consecutive Integers
1950 ◽
Vol 2
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pp. 399-405
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Keyword(s):
1. Introduction. It is the object of this paper to investigate the function γ(m), the number of representations of m in the form(1) where . It is shown that γ(m) is always equal to the number of odd divisors of m, so that for example γ(2k) = 1, this representation being the number 2k itself. From this relationship the average order of γ(m) is deduced ; this result is given in Theorem 2. By a method due to Kac [2], it is shown in §3 that the number of positive integers for which γ(m) does not exceed a rather complicated function of n and ω, a real parameter, is asymptotically nD(ω), where D(ω) is the probability integral
1970 ◽
Vol 13
(2)
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pp. 255-259
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1961 ◽
Vol 5
(1)
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pp. 35-40
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1991 ◽
Vol 43
(3)
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pp. 387-392
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1966 ◽
Vol 62
(4)
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pp. 637-642
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Keyword(s):
1958 ◽
Vol 10
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pp. 222-229
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2015 ◽
Vol 58
(4)
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pp. 858-868
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1990 ◽
Vol 42
(2)
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pp. 315-341
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Keyword(s):
2020 ◽
Vol 150
(5)
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pp. 2682-2718
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