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A333612
Numbers at which the sum of the iterated infinitary totient function (A091732) attains a record.
2
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).
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Mar 28 2020
STATUS
approved