ON THE INTEGERS RELATIVELY PRIME TO n AND ON A NUMBER-THEORETIC FUNCTION CONSIDERED BY JACOBSTHAL where on the left hand side the maximum is taken over all the integers
نویسنده
چکیده
is true. The exponent c3 can be reduced by Selberg's improvement of Brun's method, but it seems hopeless at present to decide about (3) . Jacobsthal also informed me that for r <_ 10 the value of C(r) is determined by n,.= 2, 3 . . . . p,., the p's being the consecutive primes, and that this perhaps holds for all values of r . Possibly the value of g(n,.') for n,'=n =1p,á+1 is already considerably smaller than C(r) . In a previous paper [4] I estimated g(n) for integers n of a certain special form, e .g . if n is the product of the first r consecutive primes 3 (mod 4) . It is easy to see that for almost all integers satisfying v(n)=r we have
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تاریخ انتشار 2004