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 A066685 Numbers n such that p(n) is congruent to EulerPhi(n) mod n, where p(n) denotes the n-th prime. 0

%I

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

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

%C a(12) > 10^12. - _Donovan Johnson_, Mar 14 2010

%e 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.

%e 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.

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

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

%K nonn

%O 1,2

%A _Joseph L. Pe_, Jan 11 2002

%E Examples revised by _N. J. A. Sloane_, Jan 31 2010

%E a(8)-a(11) from _Donovan Johnson_, Mar 14 2010

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Last modified September 18 03:55 EDT 2021. Contains 347505 sequences. (Running on oeis4.)