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%I #11 Sep 16 2015 13:44:15
%S 2,2,4,2,2,6,2,2,4,8,2,6,2,2,10,2,2,6,2,8,12,2,2,6,2,2,4,12,2,12,2,2,
%T 4,2,2,16,2,2,4,8,2,14,2,2,20,2,2,6,2,8,4,2,2,6,16,12,4,2,2,12,2,2,12,
%U 2,2,20,2,2,4,8,2,16,2,2,10,2,2,22,2,8,4,2,2,18,2,2,4,2,2,22,20,2,4,2,2,6,2
%N a(n) = Sum phi(k), where the sum is over the integers k which are the "non-isolated divisors" of 2n and phi(k) is the Euler totient function (phi(k) = A000010(k)). A positive divisor k of n is non-isolated if k-1 and/ or k+1 also divides n.
%C No odd integer has any non-isolated divisors.
%C a(n) = 2n - A133945(2n).
%t Table[Plus @@ EulerPhi[Select[Divisors[2n], If[ # > 1, IntegerQ[2n/(# - 1)]] || IntegerQ[2n/(# + 1)] &]], {n, 1, 80}] (* _Stefan Steinerberger_, Oct 04 2007 *)
%Y Cf. A133945.
%K nonn
%O 1,1
%A _Leroy Quet_, Oct 03 2007
%E More terms from _Stefan Steinerberger_, Oct 04 2007
%E Extended by _Ray Chandler_, May 28 2008
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