%I #10 Apr 09 2020 05:23:59
%S 1,2,3,5,7,11,17,19,23,31,41,43,47,59,71,79,83,103,107,131,139,167,
%T 223,227,263,347,359,383,467,479,563,587,659,719,839,863,887,1019,
%U 1163,1187,1223,1259,1283,1307,1319,1367,1439,1823,1979,2027,2039,2207,2447,2879
%N Numbers at which the sum of the iterated absolute Möbius divisor function (A173557) attains a record.
%C Analogous to A181659 with the absolute Möbius divisor function (A173557) instead of the Euler totient function phi (A000010).
%C The corresponding record values are 0, 1, 3, 5, 9, 15, 17, 21, 37, 39, 45, ... (see the link for more values).
%H Amiram Eldar, <a href="/A333872/b333872.txt">Table of n, a(n) for n = 1..1697</a> (terms below 10^10)
%H Amiram Eldar, <a href="/A333872/a333872.txt">Table of n, a(n), A333871(a(n)) for n = 1..1697</a>
%H Daeyeoul Kim, Umit Sarp, and Sebahattin Ikikardes, <a href="https://doi.org/10.3390/math7111083">Iterating the Sum of Möbius Divisor Function and Euler Totient Function</a>, Mathematics, Vol. 7, No. 11 (2019), pp. 1083-1094.
%t f[p_, e_] := p - 1; u[1] = 1; u[n_] := Times @@ (f @@@ FactorInteger[n]); s[n_] := Plus @@ FixedPointList[u, n] - n - 1; seq = {}; smax = -1; Do[s1 = s[n]; If[s1 > smax, smax = s1; AppendTo[seq, n]], {n, 1, 3000}]; seq
%Y Cf. A173557, A181659, A330400, A331407, A333612, A333871.
%K nonn
%O 1,2
%A _Amiram Eldar_, Apr 08 2020