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A050530 Numbers k such that k - phi(k) is prime. 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

Table of n, a(n) for n=1..55.

FORMULA

Numbers k such that A051953(k) is prime.

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A051953, A005278.

Sequence in context: A052116 A109641 A134675 * A278021 A102084 A193315

Adjacent sequences:  A050527 A050528 A050529 * A050531 A050532 A050533

KEYWORD

nonn

AUTHOR

Labos Elemer, Dec 29 1999

STATUS

approved

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Last modified May 25 03:14 EDT 2019. Contains 323539 sequences. (Running on oeis4.)