A330273 Infinitary perfect totient numbers: numbers that equal to the sum of their iterated infinitary totient function (A091732).

3, 10, 21, 44, 93, 118, 170, 320, 548, 3596, 3620, 4772, 5564, 18260, 33051, 256425, 403700, 1071129, 1790160, 2318180, 3968852, 4027375, 10001319, 11270012, 12048740, 13358121, 31741593, 46271673, 56149161, 4344134553

Offset: 1

Author

Amiram Eldar, Dec 13 2019

Keywords

• nonn
• more

Comments

The infinitary version of A082897 (perfect totient numbers), in which the infinitary totient function iphi (A091732) replaces the Euler totient function (A000010).

Examples

			10 is an infinitary perfect totient number because iphi(10) + iphi(iphi(10)) + ... = 4 + 3 + 2 + 1 = 10.
		

Crossrefs

Cf. A082897, A091732, A286067.

Programs

Mathematica

f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], ?(# == 1 &)])); iphi[1] = 1; iphi[n] := iphi[n] = Times @@ (Flatten@(f @@@ FactorInteger[n]) - 1); infPerfTotQ[n_] := Plus @@ FixedPointList[iphi@# &, n] == 2 n + 1; Select[Range[1000], infPerfTotQ]