A037171 Numbers n such that phi(n) = pi(n), i.e., A000010(n) = A000720(n).

2, 3, 4, 8, 10, 14, 20, 90

Offset

1,1

Comments

David W. Wilson and Jeffrey Shallit showed that 90 is the last term.

Leo Moser proved in 1951 that these are the only terms, but he missed the term 10. - Amiram Eldar, May 15 2017

phi(n) >= pi(n) for n >= 61, and phi(n) > pi(n) for n > 90. - Jonathan Sondow, Dec 02 2017

References

P. Birch and D. Singmaster, An elementary number theory result, Math. Soc. Newsl., 12 (1984), 10-13.

D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, p. 11.

Links

Table of n, a(n) for n=1..8.

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

Formula

A037228(a(n)) = 0. - Jonathan Sondow, Dec 02 2017

Example

phi(10)=4, pi(10)=4.
a(1)=2 since k=2 is the lowest index for which A000720(n) = A000010(n), i.e., EulerPhi(n) = PrimePi(n). - M. F. Hasler, Mar 30 2007

Maple

select(x->numtheory[phi](x)=numtheory[pi](x), [$1..999]); # M. F. Hasler, Mar 30 2007

Prog

(PARI) for(n=1, 1e5, if(primepi(n)==eulerphi(n), print(n))) /* M. F. Hasler, Mar 30 2007 */

Crossrefs

Cf. A000010, A000720, A037228, A037230.

Sequence in context: A328092 A242762 A005542 * A308811 A295296 A186417

Adjacent sequences: A037168 A037169 A037170 * A037172 A037173 A037174

Keyword

easy,nonn,fini,full

Author

Naohiro Nomoto

Status

approved