A286067 Unitary perfect totient numbers: numbers n that equal to the sum of their iterated unitary totient uphi(n).

3, 10, 21, 110, 3910, 1500988838

Offset: 1

Author

Amiram Eldar, May 01 2017

Keywords

• nonn
• more

Comments

The unitary version of A082897 (perfect totient numbers), in which the unitary totient function uphi(n) (A047994) replaces the Euler totient function phi(n) (A000010).

a(7) > 5*10^9, if it exists. - Giovanni Resta, May 06 2020

Examples

			3910 is a unitary perfect totient number because 3910 = uphi(3910) + uphi(uphi(3910)) + uphi(uphi(uphi(3910))) + ... = 1408 + 1270 + 504 + 336 + 180 + 96 + 62 + 30 + 8 + 7 + 6 + 2 + 1.
		

Crossrefs

Cf. A082897, A047994, A003271, A000010.

Programs

Mathematica

uphi[n_] := (Times @@ (Table[#[[1]]^#[[2]] - 1, {1}] & /@ FactorInteger[n]))[[1]]; kmax = 10000; a = Table[0, {kmax}]; uptns = {}; Do[e = uphi[k]; a[[k]] = e + a[[e]]; If[k == a[[k]], AppendTo[uptns , k]], {k, 2, kmax}]; uptns

Extensions

a(6) from Giovanni Resta, May 06 2020