cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Views

Author

Amiram Eldar, Apr 10 2023

Keywords

Comments

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.

Links

Crossrefs

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.

Programs

  • Mathematica
    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]

Formula

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

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

Original entry on oeis.org

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

Views

Author

Amiram Eldar, Apr 10 2023

Keywords

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

Crossrefs

Cf. A323410, A362181, A362184.
The unitary version of A100827.
Similar sequences: A097942, A361968.

Programs

  • 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]

A362488 Record values in A362487.

Original entry on oeis.org

2, 4, 6, 10, 14, 18, 22, 30, 34, 40, 48, 58, 60, 92, 136, 146, 184, 232, 240, 342, 478, 518, 638, 772, 830, 924, 1080, 1264, 1330, 1340, 1462, 1824, 2132, 2528, 2710, 3224, 3354, 4084, 4672, 4812, 4976, 5912, 6496, 7606, 8230, 8698, 11472, 12354, 16580, 19250
Offset: 1

Views

Author

Amiram Eldar, Apr 22 2023

Keywords

Crossrefs

Cf. A362484, A362487.
Similar sequences: A101373, A131934, A361971, A362184.

Programs

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

Formula

a(n) = A362485(A362487(n)).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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