A362183 Unitary highly cototient numbers: numbers k that have more solutions x to the equation A323410(x) = k than any smaller k.

0, 6, 10, 20, 31, 47, 53, 65, 77, 89, 113, 119, 149, 167, 179, 209, 293, 299, 329, 359, 389, 419, 479, 509, 599, 629, 779, 839, 989, 1049, 1139, 1259, 1469, 1559, 1649, 1679, 1889, 2099, 2309, 2729, 3149, 3359, 3569, 3989, 4289, 4409, 4619, 5249, 5459, 6089, 6509

Offset

1,2

Comments

Indices of records of A362181.

The corresponding numbers of solutions are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 17, 21, ... (A362184).

Links

Amiram Eldar, Table of n, a(n) for n = 1..96 (terms below 10^5)

Mathematica

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 = {0}; solmax=1; Do[sol = solnum[[k]]; If[sol > solmax, solmax = sol; AppendTo[s, k]], {k, 2, max}]; s]

Crossrefs

Cf. A323410, A362181, A362184.

The unitary version of A100827.

Similar sequences: A097942, A361968.

Sequence in context: A163172 A117348 A117349 * A153369 A107981 A065758

Adjacent sequences: A362180 A362181 A362182 * A362184 A362185 A362186

Keyword

nonn

Author

Amiram Eldar, Apr 10 2023

Status

approved