Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1989. 19/8. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 19)

Csóké Lajos: Sturm tételének gyakorlati alkalmazásáról.

THEOREH. There are positive absolute constants c and c , —— o which do not depend on the sequence R, such that C4) J — < log log log n + c p |R ' 1 n and t. C55 J ^ < c

o log log n d|R ' n for any n>nwhere n^ depenrls only on the sequence R. We note that similar results can be obtained if CA,B3>± but in this case the constants c and c are not absolute o ones, they depend on A and 8 We also note that in the case R =2

n~l G.Pomerance [33 obtained results for special divisors. Let E(n) « 5 1/d, where the summation is extended for positive integers d for which d|C2

n-0 and d|C2

m-l > if 0<m<n, further let FCn)=» 2 1/d, where d runs over the integers for which dJC2

n—

.1 > and d>n. Among others Pomerance proved that ECn) £ ™ exp (ci+oci

)) V log log rT j for infinitely many n and the sot of n w i th Ein) < ~ Clog ii) n ° has logarithmic density 1 for any function f for which fCn> 0 as n «--> oo > furthermore. FCn> < exp - iog n log log log n / 2 "log log nj for all large n. PROOF OF THE THEORE

M. In the proof we shall use positive real numbers c^

, c^, ... , wich are absolute constants, and