A050530 Numbers k such that k - phi(k) is prime.

4, 9, 15, 25, 33, 35, 49, 51, 65, 77, 87, 91, 95, 119, 121, 123, 143, 161, 169, 177, 185, 209, 213, 215, 217, 221, 247, 255, 259, 287, 289, 303, 321, 329, 335, 341, 361, 371, 377, 395, 403, 407, 411, 427, 435, 437, 447, 455, 469, 473, 485, 511, 515, 527, 529

Offset: 1

Author

Labos Elemer, Dec 29 1999

Keywords

• nonn

Comments

If k = p^2 is the square of a prime, then p^2 - phi(p^2) = p, so this sequence is infinite and generates all primes.

No prime p is a term of this sequence because A051953(p)=1. Other cases exist; e.g., k - phi(k) = 23 if k = 95, 119, 143, 529.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A051953, A005278.

Programs

Magma

[n: n in [1..600] | IsPrime(n-EulerPhi(n))]; // Vincenzo Librandi, Dec 18 2015

Mathematica

Select[Range[600],PrimeQ[#-EulerPhi[#]]&] (* Harvey P. Dale, Jun 23 2013 *)

Formula

Numbers k such that A051953(k) is prime.