A037230 Numbers n such that phi(n) < pi(n).

6, 12, 18, 24, 30, 42, 60

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• fini
• full

Comments

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]

Leo Moser proved in 1951 that these are the only terms. - Amiram Eldar, May 15 2017

Links

• Leo Moser, On the equation ϕ(n) = π(n), Pi Mu Epsilon Journal. Vol. 1, No. 5 (1951), pp. 177-180.

Crossrefs

Cf. A037171.

Programs

Mathematica

Select[Range[60], EulerPhi[#] < PrimePi[#] &] (* Arkadiusz Wesolowski, Dec 22 2011 *)

Extensions

Offset corrected by Arkadiusz Wesolowski, Dec 22 2011