login
Numbers k such that phi(k-1) + phi(k+1) = sigma(k)/2.
0

%I #11 Nov 10 2024 09:04:20

%S 315,351,819,3375,24921,47520,99540,107541,125631,189175,410805,

%T 763665,877365,1680855,2480555,6911079,7849479,9646395,11245365,

%U 12528165,14242800,14684055,16921191,17194365,19395025,27782160,33830685,34823075,36278649,43955955

%N Numbers k such that phi(k-1) + phi(k+1) = sigma(k)/2.

%e phi(314) + phi(316) = 156 + 156 = 312 = sigma(315)/2, so 315 is a term.

%t Select[Range[2, 10^5], EulerPhi[ # - 1] + EulerPhi[ # + 1] == (1/2)DivisorSigma[1, # ] &]

%o (PARI) is(k) = if(k < 2, 0, eulerphi(k-1) + eulerphi(k+1) == sigma(k)/2); \\ _Amiram Eldar_, Nov 10 2024

%Y Cf. A000010, A000203.

%K nonn,changed

%O 1,1

%A _Joseph L. Pe_, Oct 23 2002

%E a(8)-a(30) from _Donovan Johnson_, Mar 01 2012