A330400 Numbers at which the sum of the iterated unitary totient function (A329153) attains a record.

1, 2, 3, 4, 5, 8, 9, 16, 17, 29, 32, 41, 45, 53, 64, 73, 83, 85, 101, 113, 125, 128, 137, 153, 187, 197, 233, 257, 389, 401, 512, 577, 641, 677, 685, 703, 773, 901, 929, 977, 1153, 1193, 1493, 1537, 1553, 1657, 1697, 2047, 2048, 2313, 2897, 3089, 3137, 3593, 4001

Offset: 1

Author

Amiram Eldar, Feb 25 2020

Keywords

• nonn

Comments

Analogous to A181659 with the unitary totient function (A047994) instead of the Euler totient function phi (A000010).

The corresponding record values are 0, 1, 3, 6, 10, 16, 24, 39, 55, 70, 85, ... (see the link for more values).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..637 (terms below 2*10^9)
• Amiram Eldar, Table of n, a(n), A329153(a(n)) for n = 1..637

Crossrefs

Cf. A047994, A181659, A329153.

Programs

Mathematica

uphi[1] = 1; uphi[n_] := Times @@ (-1 + Power @@@ FactorInteger[n]); s[n_] := Plus @@ FixedPointList[uphi, n] - n - 1; seq = {}; smax = -1; Do[s1 = s[n]; If[s1 > smax, smax = s1; AppendTo[seq, n]], {n, 1, 5000}]; seq