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

1,1

Comments

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

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.

Example

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

Mathematica

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

Crossrefs

A019434 is a subsequence.

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

Sequence in context: A278138 A273870 A272060 * A058910 A373580 A307843

Adjacent sequences: A333870 A333871 A333872 * A333874 A333875 A333876

Keyword

nonn

Author

Amiram Eldar, Apr 08 2020

Status

approved