|
%I #30 May 15 2017 08:11:01
%S 6,12,18,24,30,42,60
%N Numbers n such that phi(n) < pi(n).
%C According to a note in Wacław Sierpiński's book "O stu prostych, ale trudnych zagadnieniach arytmetyki", a 1951 paper of L. Moser proves that 60 is the last term in the sequence. - _Arkadiusz Wesolowski_, Dec 22 2011 [A rough translation of the title of this book is "A hundred elementary but tough problems in arithmetic." No English translation appears to exist, but there are several later books by Sierpiński with similar titles that have been translated. I don't know if they give the Moser reference. - _N. J. A. Sloane_, Dec 26 2011]
%C Leo Moser proved in 1951 that these are the only terms. - _Amiram Eldar_, May 15 2017
%H Leo Moser, <a href="http://www.pme-math.org/journal/issues/PMEJ.Vol.1.No.5.pdf">On the equation ϕ(n) = π(n)</a>, Pi Mu Epsilon Journal. Vol. 1, No. 5 (1951), pp. 177-180.
%t Select[Range[60], EulerPhi[#] < PrimePi[#] &] (* _Arkadiusz Wesolowski_, Dec 22 2011 *)
%Y Cf. A037171.
%K nonn,fini,full
%O 1,1
%A _David W. Wilson_
%E Offset corrected by _Arkadiusz Wesolowski_, Dec 22 2011
|
