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A333872
Numbers at which the sum of the iterated absolute Möbius divisor function (A173557) attains a record.
1
1, 2, 3, 5, 7, 11, 17, 19, 23, 31, 41, 43, 47, 59, 71, 79, 83, 103, 107, 131, 139, 167, 223, 227, 263, 347, 359, 383, 467, 479, 563, 587, 659, 719, 839, 863, 887, 1019, 1163, 1187, 1223, 1259, 1283, 1307, 1319, 1367, 1439, 1823, 1979, 2027, 2039, 2207, 2447, 2879
OFFSET
1,2
COMMENTS
Analogous to A181659 with the absolute Möbius divisor function (A173557) instead of the Euler totient function phi (A000010).
The corresponding record values are 0, 1, 3, 5, 9, 15, 17, 21, 37, 39, 45, ... (see the link for more values).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1697 (terms below 10^10)
Daeyeoul Kim, Umit Sarp, and Sebahattin Ikikardes, Iterating the Sum of Möbius Divisor Function and Euler Totient Function, Mathematics, Vol. 7, No. 11 (2019), pp. 1083-1094.
MATHEMATICA
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Apr 08 2020
STATUS
approved