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A065139 Numbers n such that the sum of prime(n) and pi(n) is divisible by n. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A020895 A174247 A321322 * 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

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Last modified September 24 04:19 EDT 2020. Contains 337317 sequences. (Running on oeis4.)