By Waclaw Sierpinski

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**Extra resources for 250 problems in elementary number theory**

**Example text**

49) and Theorem 06, we have 0( -,y)»x/gdlogy moreover the condition qd < x is redundant. So x 1 1 1 R» log y,aa,ay/Q

First, following Erdos & Katai (1971) we define M(n, z) _ Y µ(d), M(n) = sup JM(n, z)J. 20) held for j > fi(n) then M(n) < hence we should have But H. p. - log 2 K' = log (1 -1/log 3) confirming a conjecture of Erdos & Hall (1980). 20) is as follows. p. 22) 22 1 The normal distribution of the prime factors (Erd6s(1966)). For a more precise result, see Bovey (1977). 17)). p. Notice that this implies a real difference between the two orderings of the divisors mentioned in the introduction. A consequence of Theorem 12 is the following result about the jth divisor dj(n).

20) i