A333612 Numbers at which the sum of the iterated infinitary totient function (A091732) attains a record.

1, 2, 3, 4, 5, 9, 11, 13, 16, 17, 29, 37, 47, 49, 53, 81, 101, 107, 113, 149, 173, 197, 257, 389, 401, 509, 529, 531, 557, 593, 677, 701, 747, 773, 829, 963, 977, 1109, 1297, 1493, 1675, 1733, 1901, 2417, 2761, 2837, 3089, 3313, 3329, 3413, 3467, 3677, 3803, 3989

Offset

1,2

Comments

Analogous to A181659 with the infinitary totient function A091732 instead of the Euler totient function phi (A000010).

The corresponding record values are 0, 1, 3, 6, 10, 14, 20, 21, 29, 45, ... (see the link for more values).

Links

Amiram Eldar, Table of n, a(n) for n = 1..500

Amiram Eldar, Table of n, a(n), A333611(a(n)) for n=1..500

Mathematica

f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], 1])); iphi[1] = 1; iphi[n_] := Times @@ (Flatten@(f @@@ FactorInteger[n]) - 1); s[n_] := Plus @@ NestWhileList[iphi, n, # != 1 &] - n; seq = {}; smax = -1; Do[s1 = s[n];  If[s1 > smax, smax = s1; AppendTo[seq, n]], {n, 1, 10^5}]; seq

Crossrefs

Cf. A091732, A181659, A330400, A331407, A333611.

Sequence in context: A143827 A100797 A139441 * A362025 A093305 A065817

Adjacent sequences: A333609 A333610 A333611 * A333613 A333614 A333615

Keyword

nonn

Author

Amiram Eldar, Mar 28 2020

Status

approved