A065139 Numbers n such that the sum of prime(n) and pi(n) is divisible by n.

1, 2, 7, 9, 23, 57, 149, 368, 921, 5863, 14531, 36087, 36255, 36257, 233084, 1505984, 1151321194, 1151321361, 7826138122, 967823489175, 967823489458, 967823489477, 967823489490, 967823489491, 2545928465925, 123116092093107, 123116092093185, 123116092094024

Offset

1,2

Links

Giovanni Resta, Table of n, a(n) for n = 1..33

Formula

Solutions to pi(x) + prime(x) = A000720(x) + A000040(x) = 0 (mod x).

Example

p(233084) = 3242497, Pi(233084) = 20679; sum = 3263176 = 14*233084; order of quotient is log(n).
(prime(1505984) + pi(1505984))/1505984 = (23981141 + 114603)/1505984 = 16.

Mathematica

Do[ If[ IntegerQ[ (Prime[n] + PrimePi[n]) /n ], Print[n]], {n, 1, 5*10^7} ]
Select[ Range[10^8], IntegerQ[(Prime[ # ] + PrimePi[ # ])/ # ] & ]

Prog

(PARI) k=0; n=0; forprime(p=2, 4e9, if(isprime(n++), k++); if((k+p)%n==0, print1(n", "))) \\ Charles R Greathouse IV, Aug 21 2011

Crossrefs

Cf. A000040, A000720, A006988.

Sequence in context: A343963 A321322 A343495 * A093916 A042451 A042929

Adjacent sequences: A065136 A065137 A065138 * A065140 A065141 A065142

Keyword

nonn

Author

Labos Elemer, Oct 16 2001

Extensions

a(17)-a(19) from Donovan Johnson, Aug 21 2011

a(20)-a(28) from Giovanni Resta, Oct 15 2019

Status

approved