A333871 Sum of the iterated absolute Möbius divisor function (A173557).

0, 1, 3, 1, 5, 3, 9, 1, 3, 5, 15, 3, 15, 9, 9, 1, 17, 3, 21, 5, 15, 15, 37, 3, 5, 15, 3, 9, 37, 9, 39, 1, 25, 17, 27, 3, 39, 21, 27, 5, 45, 15, 57, 15, 9, 37, 83, 3, 9, 5, 33, 15, 67, 3, 45, 9, 39, 37, 95, 9, 69, 39, 15, 1, 51, 25, 91, 17, 59, 27, 97, 3, 75, 39

Offset: 1

Author

Amiram Eldar, Apr 08 2020

Keywords

• nonn

Comments

Analogous to A092693 with the absolute Möbius divisor function (A173557) instead of the Euler totient function phi (A000010).

Examples

			a(3) = A173557(3) + A173557(A173557(3)) = 2 + 1 = 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Daeyeoul Kim, Umit Sarp, and Sebahattin Ikikardes, Iterating the Sum of Möbius Divisor Function and Euler Totient Function, Mathematics, Vol. 7, No. 11 (2019), pp. 1083-1094.

Crossrefs

Cf. A092693, A173557, A333870.

Programs

Mathematica

f[p_, e_] := p - 1; u[1] = 1; u[n_] := Times @@ (f @@@ FactorInteger[n]); a[n_] := Plus @@ FixedPointList[u, n] - n - 1 ; Array[a, 100]