A329153 Sum of the iterated unitary totient function (A047994).

0, 1, 3, 6, 10, 3, 9, 16, 24, 10, 20, 9, 21, 9, 24, 39, 55, 24, 42, 21, 21, 20, 42, 23, 47, 21, 47, 42, 70, 24, 54, 85, 41, 55, 47, 47, 83, 42, 47, 70, 110, 21, 63, 54, 117, 42, 88, 54, 102, 47, 117, 83, 135, 47, 110, 63, 83, 70, 128, 47, 107, 54, 102, 165, 102

Offset: 1

Author

Amiram Eldar, Feb 25 2020

Keywords

• nonn

Comments

Analogous to A092693 with the unitary totient function uphi instead of the Euler totient function phi (A000010).

Examples

			a(4) = uphi(4) + uphi(uphi(4)) + uphi(uphi(uphi(4))) = 3 + 2 + 1 = 6.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003271, A047994, A049865, A092693, A225172, A225173, A286067.

Programs

Mathematica

uphi[1] = 1; uphi[n_] := Times @@ (-1 + Power @@@ FactorInteger[n]); Table[Plus @@ FixedPointList[uphi, n] - n - 1, {n, 1, 100}]

Formula

a(n) = n for n in A286067.