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

1,1

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

Links

Table of n, a(n) for n=1..6.

Example

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.

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

Crossrefs

Cf. A082897, A047994, A003271, A000010.

Sequence in context: A139116 A373081 A120109 * A337623 A158030 A068082

Adjacent sequences: A286064 A286065 A286066 * A286068 A286069 A286070

Keyword

nonn,more

Author

Amiram Eldar, May 01 2017

Extensions

a(6) from Giovanni Resta, May 06 2020

Status

approved