A286233 - OEIS

%I #6 May 04 2017 16:20:49

%S 579,639,14911,18207,38575,47223,310399,492855,16632919,20238207,

%T 34696495,37400607,37852351,52463103,84250111,122992023

%N Amicable totient numbers: pairs of numbers (m, n) such that n = A092693(m) and m = A092693(n).

%C Analogous to amicable pairs (A063990) as perfect totient numbers (A082897) are analogous to perfect numbers (A000396).

%C The sequence lists the numbers in increasing order. The first 8 pairs (m, n) are adjacent to each other in the list.

%C No other terms below 10^9.

%e A092693(579) = phi(579) + phi(phi(579)) + ... = 384 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 639, and A092693(639) = phi(639) + phi(phi(639)) + ... = 420 + 96 + 32 + 16 + 8 + 4 + 2 + 1 = 579.

%t totSum[n_] := Plus @@ FixedPointList[EulerPhi@# &, n] - n - 1; amicableTotQ[n_] := If[Nest[totSum, n, 2] == n && totSum[n] != n, True, False]; Select[Range[10^9], amicableTotQ[#] &]

%Y Cf. A092693, A082897, A091847.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, May 04 2017