A333873 Numbers that equal to the sum of their iterated absolute Möbius divisor function (A173557).

3, 5, 17, 257, 413, 611, 1391, 1589, 1903, 2327, 5599, 27959, 29623, 36647, 36983, 38863, 42851, 43919, 46463, 49513, 65537, 76759, 82969, 86567, 88759, 96839, 111179, 116479, 129307, 171191, 184979, 213041, 277619, 301157, 310519, 346151, 362263, 372227, 375167

Offset: 1

Author

Amiram Eldar, Apr 08 2020

Keywords

• nonn

Comments

A variant of A082897 (perfect totient numbers) in which the absolute Möbius divisor function (A173557) replaces the Euler totient function (A000010).

Examples

			5 is a term since A173557(5) = 4, A173557(4) = 1, and 4 + 1 = 5.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..350 (terms below 4*10^9)
• 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

A019434 is a subsequence.

Cf. A082897, A173557, A286067, A330273, A333871.

Programs

Mathematica

f[p_, e_] := p - 1; u[1] = 1; u[n_] := Times @@ (f @@@ FactorInteger[n]); Select[Range[10^4], Plus @@ FixedPointList[u, #] == 2*# + 1 &]