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

1,2

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

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

Crossrefs

Cf. A047994, A181659, A329153.

Sequence in context: A287117 A286431 A015931 * A306044 A263581 A120430

Adjacent sequences: A330397 A330398 A330399 * A330401 A330402 A330403

Keyword

nonn

Author

Amiram Eldar, Feb 25 2020

Status

approved