A286233 Amicable totient numbers: pairs of numbers (m, n) such that n = A092693(m) and m = A092693(n).

579, 639, 14911, 18207, 38575, 47223, 310399, 492855, 16632919, 20238207, 34696495, 37400607, 37852351, 52463103, 84250111, 122992023

Offset

1,1

Comments

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

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

No other terms below 10^9.

Links

Table of n, a(n) for n=1..16.

Example

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.

Mathematica

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[#] &]

Crossrefs

Cf. A092693, A082897, A091847.

Sequence in context: A035754 A107550 A097768 * A073735 A250727 A252985

Adjacent sequences: A286230 A286231 A286232 * A286234 A286235 A286236

Keyword

nonn,more

Author

Amiram Eldar, May 04 2017

Status

approved