A333871 -id:A333871 - cp's OEIS frontend

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

Amiram Eldar, Apr 08 2020

nonn

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).

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.

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

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

A333873 Numbers that equal to the sum of their iterated absolute Möbius divisor function (A173557).

Original entry on oeis.org

3, 5, 17, 257, 413, 611, 1391, 1589, 1903, 2327, 5599, 27959, 29623, 36647, 36983, 38863, 42851, 43919, 46463, 49513, 65537, 76759, 82969, 86567, 88759, 96839, 111179, 116479, 129307, 171191, 184979, 213041, 277619, 301157, 310519, 346151, 362263, 372227, 375167

Offset: 1

Amiram Eldar, Apr 08 2020

nonn

A variant of A082897 (perfect totient numbers) in which the absolute Möbius divisor function (A173557) replaces the Euler totient function (A000010).

			5 is a term since A173557(5) = 4, A173557(4) = 1, and 4 + 1 = 5.

Amiram Eldar, Table of n, a(n) for n = 1..350 (terms below 4*10^9)
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.

A019434 is a subsequence.

Cf. A082897, A173557, A286067, A330273, A333871.

f[p_, e_] := p - 1; u[1] = 1; u[n_] := Times @@ (f @@@ FactorInteger[n]); Select[Range[10^4], Plus @@ FixedPointList[u, #] == 2*# + 1 &]

cp's OEIS Frontend

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

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