A233189 Numbers n such that phi(n) + pi(n) = n+1.

3, 9, 55, 65, 95, 145, 155, 185, 205, 2779, 2863, 21199, 174691, 174779, 1277809, 1301989, 1302457, 1930091, 2554873, 8170013, 70111213, 70111247, 514269523, 514269599, 27788312339, 341964217733, 358200797989, 763730325367, 1975633764583

Offset

1,1

Comments

a(30) > 2*10^12. - Giovanni Resta, Mar 31 2017

Links

Table of n, a(n) for n=1..29.

Example

a(3)= 55: n= 55: phi(n)+pi(n)= 40+16= 56 which equals n+1= 55+1= 56.
a(4)= 65: n= 65: phi(n)+pi(n)= 48+18= 66 which equals n+1= 65+1= 66.

Maple

with(numtheory): KD:= proc() local a, b; a:= n+1; b:=phi(n) +pi(n);  if a=b then  RETURN (n);  fi; end:  seq(KD(), n=1..10000000);

Mathematica

Do[If [ PrimePi[n]+EulerPhi[n] == n+1, Print[n]], {n, 100000000}]

Prog

(PARI) isok(n) = eulerphi(n)+primepi(n) == n + 1; \\ Michel Marcus, Apr 01 2017

Crossrefs

Cf. A000203 (sigma(n): sum of divisors of n).

Cf. A000720 (pi(n): number of primes <= n).

Cf. A037170 (numbers n: pi(n) + phi(n)= n).

Sequence in context: A025226 A001194 A032179 * A175117 A245117 A183303

Adjacent sequences: A233186 A233187 A233188 * A233190 A233191 A233192

Keyword

nonn,more

Author

K. D. Bajpai, Dec 05 2013

Extensions

a(23)-a(24) from T. D. Noe, Dec 05 2013

a(25)-a(29) from Giovanni Resta, Mar 31 2017

Status

approved