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%I #12 Oct 30 2019 16:11:54
%S 1,0,3,2,5,2,7,6,9,8,11,6,13,12,15,14,17,14,19,12,21,20,23,18,25,24,
%T 27,26,29,20,31,30,33,32,35,30,37,36,39,32,41,30,43,42,45,44,47,42,49,
%U 48,51,50,53,50,55,44,57,56,59,48,61,60,63,62,65,62,67,66,69,68,71,56,73
%N Sum phi(k), where the sum is over the integers k which are the "isolated divisors" of n and phi(k) is the Euler totient function (phi(k) = A000010(k)). A positive divisor, k, of n is isolated if neither (k-1) nor (k+1) divides n.
%C Every divisor of an odd integer is an "isolated divisor."
%C a(2n+1) = 2n+1; a(2n) = 2n - A133946(n) .
%t g[n_] := Block[{d = Divisors[n]},Select[d, FreeQ[d, # - 1] && FreeQ[d, # + 1] &]];Table[Plus @@ EulerPhi /@ g[n], {n, 100}] (* _Ray Chandler_, May 28 2008 *)
%Y Cf. A133946.
%K nonn
%O 1,3
%A _Leroy Quet_, Sep 30 2007
%E Extended by _Ray Chandler_, May 28 2008