OFFSET
1,1
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..500
EXAMPLE
Since (p+1)(p-1) + 2(p+1) = p^2 + 2p + 1 = (p+1)^2 is a square, all primes are solutions. For n = 28, sigma(28) = 56, phi(28) = 12, 56*12 + 2*56 = 784 = 28*28, so 28 is a composite solution.
MATHEMATICA
Select[Range@ 30000, Function[n, And[CompositeQ@ n, IntegerQ@ Sqrt[# EulerPhi@ n + 2 #] &@ DivisorSigma[1, n]]]] (* Michael De Vlieger, Mar 18 2017 *)
PROG
(PARI) { n=0; for (m=1, 10^9, if (isprime(m), next); s=sigma(m)*eulerphi(m) + 2*sigma(m); if (issquare(s), write("b065655.txt", n++, " ", m); if (n==500, return)) ) } \\ Harry J. Smith, Oct 25 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 12 2001
STATUS
approved