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Numbers n such that phi(n) + phi(n+1) = sigma(n)/2.
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%I #11 Aug 15 2019 06:47:54

%S 56,456,476,828,846,1196,2060,2780,4484,7530,9174,11420,11475,11865,

%T 13454,22154,34916,35385,52185,67308,105798,140895,168872,190840,

%U 219852,241892,244074,267225,303834,317564,330484,335440,460292,580970,658515

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

%H Donovan Johnson, <a href="/A076647/b076647.txt">Table of n, a(n) for n = 1..200</a>

%e phi(56) + phi(57) = 24 + 36 = 60 = 1/2 sigma(56), so 56 is a term of the sequence.

%p with(numtheory): p:=proc(n) if phi(n)+phi(n+1)=sigma(n)/2 then n else fi end: seq(p(n),n=1..2500000); # _Emeric Deutsch_, Sep 02 2005

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

%o (PARI) isok(n) = eulerphi(n) + eulerphi(n+1) == sigma(n)/2; \\ _Michel Marcus_, Aug 15 2019

%Y Cf. A092404.

%K nonn

%O 1,1

%A _Joseph L. Pe_, Oct 23 2002

%E More terms from _Emeric Deutsch_, Sep 02 2005