A066685 Numbers n such that p(n) is congruent to EulerPhi(n) mod n, where p(n) denotes the n-th prime.

1, 2, 3, 789, 40087, 238717, 251737, 7847315, 69673727, 2283427137, 2664260621

Offset

1,2

Comments

a(12) > 10^12. - Donovan Johnson, Mar 14 2010

Links

Table of n, a(n) for n=1..11.

Example

p(1) = 2 is congruent to 0 mod 1, and EulerPhi(1) = 1 is congruent to 0 mod 1, so 1 is a term of the sequence.
p(3) = 5 is congruent to 2 mod 3, and EulerPhi(3) = 2 is congruent to 2 mod 3, so 3 is a term of the sequence.

Mathematica

Select[ Range[ 1, 10^6 ], Mod[ EulerPhi[ # ], # ] == Mod[ Prime[ # ], # ] & ]

Prog

(PARI) print1(n=1); forprime(p=3, 1e9, if(p%n++==eulerphi(n), print1(", "n))) \\ Charles R Greathouse IV, Mar 04 2017

Crossrefs

Sequence in context: A226148 A108332 A256115 * A076155 A352537 A136611

Adjacent sequences: A066682 A066683 A066684 * A066686 A066687 A066688

Keyword

nonn

Author

Joseph L. Pe, Jan 11 2002

Extensions

Examples revised by N. J. A. Sloane, Jan 31 2010

a(8)-a(11) from Donovan Johnson, Mar 14 2010

Status

approved