A331407 Numbers at which the sum of the iterated exponential totient function (A331273) attains a record.

1, 2, 8, 32, 128, 864, 3456, 7776, 31104, 279936, 497664, 1990656, 4478976, 17915904, 62208000, 97200000, 559872000, 874800000, 1555200000, 6220800000, 13996800000, 55987200000

Offset: 1

Author

Amiram Eldar, Feb 25 2020

Keywords

• nonn
• more

Comments

Analogous to A181659 with the exponential totient function (A072911) instead of the Euler totient function phi (A000010).

The corresponding record values are 0, 1, 3, 5, 7, 11, 13, 19, 27, 37, 43, 51, 61, 75, 83, 101, 123, 147, 165, 195, 243, 293, ...

Crossrefs

Cf. A072911, A181659, A331273.

Programs

Mathematica

ephi[n_] := Times @@ EulerPhi[FactorInteger[n][[;; , 2]]]; s[n_] := Plus @@ FixedPointList[ephi, n] - n - 1; seq = {}; smax = -1; Do[s1 = s[n]; If[s1 > smax, smax = s1; AppendTo[seq, n]], {n, 1, 5000}]; seq