A362183 -id:A362183 - cp's OEIS frontend

A362184 Record values in A362183.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 17, 21, 23, 25, 26, 27, 31, 33, 34, 37, 38, 45, 49, 54, 59, 62, 64, 71, 80, 81, 84, 92, 99, 106, 122, 137, 145, 147, 167, 174, 180, 183, 203, 211, 231, 232, 251, 253, 283, 289, 306, 318, 342, 362, 378, 410, 412, 453

Offset: 1

Amiram Eldar, Apr 10 2023

nonn

Amiram Eldar, Table of n, a(n) for n = 1..96

The unitary version of A101373.
Cf. A362181, A362183.
Similar sequences: A131934, A361971.

ucototient[n_] := n - Times @@ (Power @@@ FactorInteger[n] - 1); ucototient[1] = 0; With[{max = 300}, solnum = Table[0, {n, 1, max}]; Do[If[(i = ucototient[k]) <= max, solnum[[i]]++], {k, 2, max^2}]; s = {1}; solmax=1; Do[sol = solnum[[k]]; If[sol > solmax, solmax = sol; AppendTo[s, sol]], {k, 2, max}]; s]

a(n) = A362181(A362183(n)).

A362181 Number of numbers k such that A323410(k) = n.

Original entry on oeis.org

0, 0, 1, 0, 2, 1, 2, 1, 3, 1, 3, 2, 3, 3, 2, 2, 3, 3, 4, 3, 3, 3, 3, 3, 4, 4, 3, 3, 4, 5, 4, 5, 4, 5, 3, 4, 4, 5, 3, 5, 3, 5, 5, 5, 4, 6, 4, 6, 4, 6, 2, 7, 4, 6, 4, 6, 3, 7, 3, 5, 4, 6, 3, 8, 2, 6, 6, 7, 4, 8, 4, 6, 6, 7, 3, 9, 4, 7, 4, 5, 5, 9, 6, 9, 4, 7, 3

Offset: 2

Amiram Eldar, Apr 10 2023

nonn

The offset is 2 since A323410(p) = 1 for all prime powers p (A246655).

a(0) = 1, since there is only one solution, x = 1, to A323410(x) = 0.

Amiram Eldar, Table of n, a(n) for n = 2..10000

Row lengths of A362180.
The unitary version of A063740.
Cf. A246655, A323410, A362182 (positions of 0's), A362183 (indices of records), A362184, A362185 (positions of 1's), A362186.
Similar sequences: A014197, A361967.

ucototient[n_] := n - Times @@ (Power @@@ FactorInteger[n] - 1); ucototient[1] = 0; With[{max = 100}, ucot = Table[ucototient[n], {n, 1, max^2}]; Table[Length[Position[ucot, n]], {n, 2, max}] // Flatten]

a(A362182(n)) = 0.
a(A362185(n)) = 1.
a(A362186(n)) = n.

A362487 Infinitary highly totient numbers: numbers k that have more solutions x to the equation iphi(x) = k than any smaller k, where iphi is the infinitary totient function A091732.

Original entry on oeis.org

1, 6, 12, 24, 48, 96, 144, 240, 288, 480, 576, 720, 1152, 1440, 2880, 4320, 5760, 8640, 11520, 17280, 34560, 51840, 69120, 103680, 120960, 172800, 207360, 241920, 345600, 362880, 414720, 483840, 725760, 967680, 1209600, 1451520, 1935360, 2419200, 2903040, 3628800

Offset: 1

Amiram Eldar, Apr 22 2023

nonn

Indices of records of A362485.

The corresponding numbers of solutions are 2, 4, 6, 10, 14, 18, 22, ... (A362488).

Amiram Eldar, Table of n, a(n) for n = 1..50

Cf. A091732, A362484, A362485, A362486, A362488.

Similar sequences: A097942, A100827, A361968, A362183.

solnum[n_] := Length[invIPhi[n]]; seq[kmax_] := Module[{s = {}, solmax=0}, Do[sol = solnum[k]; If[sol > solmax, solmax = sol; AppendTo[s, k]], {k, 1, kmax}]; s]; seq[10^4] (* using the function invIPhi from A362484 *)

cp's OEIS Frontend

A362184 Record values in A362183.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A362181 Number of numbers k such that A323410(k) = n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A362487 Infinitary highly totient numbers: numbers k that have more solutions x to the equation iphi(x) = k than any smaller k, where iphi is the infinitary totient function A091732.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica