A333872 Numbers at which the sum of the iterated absolute Möbius divisor function (A173557) attains a record.

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)

Amiram Eldar, Table of n, a(n), A333871(a(n)) for n = 1..1697

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

Cf. A173557, A181659, A330400, A331407, A333612, A333871.

Sequence in context: A181562 A095365 A042989 * A302493 A188713 A280996

Adjacent sequences: A333869 A333870 A333871 * A333873 A333874 A333875

Keyword

nonn

Author

Amiram Eldar, Apr 08 2020

Status

approved