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A286233 Amicable totient numbers: pairs of numbers (m, n) such that n = A092693(m) and m = A092693(n). 0
579, 639, 14911, 18207, 38575, 47223, 310399, 492855, 16632919, 20238207, 34696495, 37400607, 37852351, 52463103, 84250111, 122992023 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 20 17:09 EST 2019. Contains 329337 sequences. (Running on oeis4.)