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A063530
Numbers k such that phi(k)+1 is a square.
4
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
1,1
COMMENTS
Numbers k such that A000010(k) = -1 + m^2 for some m.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)
EXAMPLE
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.
MATHEMATICA
Select[Range[400], IntegerQ[Sqrt[1+EulerPhi[#]]]&] (* Harvey P. Dale, Jul 31 2020 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Aug 02 2001
STATUS
approved