A330400 -id:A330400 - cp's OEIS frontend

A333612 Numbers at which the sum of the iterated infinitary totient function (A091732) attains a record.

1, 2, 3, 4, 5, 9, 11, 13, 16, 17, 29, 37, 47, 49, 53, 81, 101, 107, 113, 149, 173, 197, 257, 389, 401, 509, 529, 531, 557, 593, 677, 701, 747, 773, 829, 963, 977, 1109, 1297, 1493, 1675, 1733, 1901, 2417, 2761, 2837, 3089, 3313, 3329, 3413, 3467, 3677, 3803, 3989

Offset: 1

Amiram Eldar, Mar 28 2020

nonn

Analogous to A181659 with the infinitary totient function A091732 instead of the Euler totient function phi (A000010).

The corresponding record values are 0, 1, 3, 6, 10, 14, 20, 21, 29, 45, ... (see the link for more values).

Amiram Eldar, Table of n, a(n) for n = 1..500
Amiram Eldar, Table of n, a(n), A333611(a(n)) for n=1..500

Cf. A091732, A181659, A330400, A331407, A333611.

f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], 1])); iphi[1] = 1; iphi[n_] := Times @@ (Flatten@(f @@@ FactorInteger[n]) - 1); s[n_] := Plus @@ NestWhileList[iphi, n, # != 1 &] - n; seq = {}; smax = -1; Do[s1 = s[n];  If[s1 > smax, smax = s1; AppendTo[seq, n]], {n, 1, 10^5}]; seq

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

Original entry on oeis.org

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

cp's OEIS Frontend

A333612 Numbers at which the sum of the iterated infinitary totient function (A091732) attains a record.

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