A362185 -id:A362185 - cp's OEIS frontend

A362211 a(n) is the unique solution to A323410(x) = A362185(n).

1, 6, 15, 21, 35, 11392, 1688, 10048, 53632, 101632, 5272, 2632, 6616, 50368, 1386, 102016, 1716, 1722, 161152, 4356, 11992, 92992, 4716, 101312, 589312, 2634, 644608, 3538, 3778, 898048, 30896, 16312, 3610, 3510, 4702, 1432576, 4626, 606976, 8908, 3738, 343936

Offset: 1

Amiram Eldar, Apr 11 2023

nonn

Amiram Eldar, Table of n, a(n) for n = 1..2335

Cf. A323410, A362185.

Similar sequences: A131826, A362212.

ucototient[n_] := n - Times @@ (Power @@@ FactorInteger[n] - 1); ucototient[1] = 0; With[{max = 3000}, sol = solnum = Table[0, {n, 1, max}]; Do[If[(i = ucototient[k]) <= max, sol[[i]] = k; solnum[[i]]++], {k, 2, max^2}]; Join[{1}, sol[[Position[solnum, 1] // Flatten]]]]

A323410(a(n)) = A362185(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.

A362664 Numbers k with exactly two solutions x to the equation iphi(x) = k, where iphi is the infinitary totient function A091732.

Original entry on oeis.org

1, 2, 3, 4, 10, 15, 20, 22, 28, 42, 44, 45, 46, 52, 54, 56, 58, 70, 78, 82, 92, 100, 102, 104, 106, 116, 130, 136, 140, 148, 162, 164, 166, 172, 174, 178, 184, 190, 196, 200, 204, 208, 212, 220, 222, 226, 228, 234, 238, 246, 250, 255, 260, 262, 268, 272, 282, 292, 296

Offset: 1

Amiram Eldar, Apr 29 2023

nonn

Numbers k such that A362485(k) = 2.

There are no numbers k with a single solution to iphi(x) = k, because if iphi(x) = k, and A007814(x) is even, then 2*x is also a solution, i.e., iphi(2*x) = k.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A007814, A091732, A362484, A362485.

Similar sequences: A361969, A362185.

Select[Range[300], Length[invIPhi[#]] == 2 &] (* using the function invIPhi from A362484 *)

cp's OEIS Frontend

A362211 a(n) is the unique solution to A323410(x) = A362185(n).

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

A362664 Numbers k with exactly two solutions x to the equation iphi(x) = k, where iphi is the infinitary totient function A091732.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica