OFFSET
1,2
LINKS
Harry J. Smith and Donovan Johnson, Table of n, a(n) for n = 1..5000 (first 500 terms from Harry J. Smith)
FORMULA
EXAMPLE
n = 5396, phi(n) = 2520, sigma(n) = 10080, arithmetic mean = 6300, geometric mean = 5040, harmonic mean = 4032; 67 cases < 10^6.
MATHEMATICA
Do[s = EulerPhi[n]*DivisorSigma[1, n]; z = (EulerPhi[n]+DivisorSigma[1, n])/2; u = h[n]; If[IntegerQ[Sqrt[s]]&&IntegerQ[z]&&IntegerQ[u], Print[n]], {n, 1, 1000000}]
PROG
(PARI) { n=0; for (m=1, 10^9, e=eulerphi(m); s=sigma(m); if (!issquare(e*s), next); h=(2*e*s)/(e + s); if (frac(h) != 0, next); if (frac((e + s)/2) != 0, next); write("b065146.txt", n++, " ", m); if (n==500, return) ) } \\ Harry J. Smith, Oct 12 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Oct 18 2001
STATUS
approved