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Numbers k such that phi(k) + 1 is prime.
12

%I #30 Sep 08 2022 08:44:53

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,17,18,19,21,22,23,26,27,28,29,31,32,

%T 34,36,37,38,40,41,42,43,46,47,48,49,53,54,55,57,58,59,60,61,62,63,67,

%U 71,73,74,75,76,77,79,82,83,86,88,89,91,93,94,95,97,98,99,100,101,103

%N Numbers k such that phi(k) + 1 is prime.

%C Positive integers k for which values of A039649(k) are primes. - _Vladimir Shevelev_, May 10 2008

%C For every prime p, the numbers p and 2p are terms of this sequence. - _Vladimir Shevelev_, May 10 2008

%C Union of A000040 and A066071. - _Ray Chandler_, May 26 2008

%H Antti Karttunen, <a href="/A039698/b039698.txt">Table of n, a(n) for n = 1..26197</a> (first 1000 terms from Vincenzo Librandi)

%e phi(10)+1 = 4+1 = 5, a prime number, so 10 is a term.

%t Select[Range[300], PrimeQ[EulerPhi[#] + 1]&] (* _Vincenzo Librandi_, Aug 13 2013 *)

%o (Magma) [n: n in [1..200] | IsPrime(EulerPhi(n)+1)]; // _Vincenzo Librandi_, Aug 13 2013

%Y Cf. A000010, A000040, A006093, A039649, A066071, A007614.

%Y Cf. A039689 (complement), A296079 (characteristic function).

%Y Cf. also A065512, A078892, A263028, A248792.

%K nonn,easy

%O 1,2

%A _Olivier GĂ©rard_

%E Edited by _N. J. A. Sloane_, May 21 2008 at the suggestion of _R. J. Mathar_