A063530 Numbers k such that phi(k)+1 is a square.

15, 16, 20, 24, 30, 35, 39, 45, 52, 56, 65, 70, 72, 78, 84, 90, 104, 105, 112, 123, 130, 140, 143, 144, 155, 156, 164, 165, 168, 175, 176, 180, 183, 200, 203, 210, 215, 220, 225, 231, 244, 245, 246, 248, 261, 264, 286, 300, 308, 310, 323, 330, 339, 344, 350

Offset: 1

Author

Labos Elemer, Aug 02 2001

Keywords

• nonn

Comments

Numbers k such that A000010(k) = -1 + m^2 for some m.

Examples

			If k = p*(p+2), a product of twin primes (from A037074), then k is in the sequence. The corresponding square is p^2. Other solutions are k = {56,72,78,84}, since phi(k) + 1 = 25 for all. Also phi(123) + 1 = 9^2, the square of a composite.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)

Crossrefs

Cf. A000010, A037074, A039649.

Programs

Mathematica

Select[Range[400],IntegerQ[Sqrt[1+EulerPhi[#]]]&] (* Harvey P. Dale, Jul 31 2020 *)

PARI

{ n=0; for (a=1, 10^9, if (issquare(eulerphi(a) + 1), write("b063530.txt", n++, " ", a); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 25 2009