OFFSET
1,1
COMMENTS
Discovered while proving that phi(n) > 2pi(n) for all n, to prove a conjecture on www.primepuzzles.net. The conjecture stated that for all sufficiently large even n, n is the sum of two coprime composite numbers. This is in fact true for all even n > 210. For more details email the author.
Terms from 120120 to 2282280 have been determined empirically, by examining the ratio phi(k)/pi(k) for k up to 10^9. - Giovanni Resta, Mar 29 2017
LINKS
C. Rivera, Perry's conjecture
EXAMPLE
For all n > 90090, phi(n)/pi(n) > 2 > 17280/8726 = 1.9803.
MATHEMATICA
up = 210211; f[n_] := If[n==1, 0, EulerPhi[n]/PrimePi[n]]; T = Array[f, up]; Do[T[[k]] = Min[T[[k]], T[[k + 1]]], {k, up - 1, 2, -1}]; Select[ Range[2, up-1], T[[#]] < T[[# + 1]] &] (* Giovanni Resta, Mar 29 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Luke Pebody (ltp1000(AT)hermes.cam.ac.uk), Feb 13 2003
EXTENSIONS
Data corrected and extended by Giovanni Resta, Mar 29 2017
STATUS
approved