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%I #16 Feb 26 2020 00:30:21
%S 1,2,3,4,5,8,9,16,17,29,32,41,45,53,64,73,83,85,101,113,125,128,137,
%T 153,187,197,233,257,389,401,512,577,641,677,685,703,773,901,929,977,
%U 1153,1193,1493,1537,1553,1657,1697,2047,2048,2313,2897,3089,3137,3593,4001
%N Numbers at which the sum of the iterated unitary totient function (A329153) attains a record.
%C Analogous to A181659 with the unitary totient function (A047994) instead of the Euler totient function phi (A000010).
%C The corresponding record values are 0, 1, 3, 6, 10, 16, 24, 39, 55, 70, 85, ... (see the link for more values).
%H Amiram Eldar, <a href="/A330400/b330400.txt">Table of n, a(n) for n = 1..637</a> (terms below 2*10^9)
%H Amiram Eldar, <a href="/A330400/a330400.txt">Table of n, a(n), A329153(a(n)) for n = 1..637</a>
%t 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
%Y Cf. A047994, A181659, A329153.
%K nonn
%O 1,2
%A _Amiram Eldar_, Feb 25 2020
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