A362182 -id:A362182 - cp's OEIS frontend

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

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.

A362486 Infinitary nontotient numbers: values not in the range of the infinitary totient function iphi (A091732).

Original entry on oeis.org

5, 7, 9, 11, 13, 14, 17, 19, 21, 23, 25, 26, 27, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 47, 49, 50, 51, 53, 55, 57, 59, 61, 62, 63, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 98, 99, 101, 103, 105, 107, 109, 110, 111

Offset: 1

Amiram Eldar, Apr 22 2023

nonn

Numbers k such that A091732(x) = k has no solution, i.e., A362485(k) = 0.

Most of the odd numbers are in this sequence. Odd numbers that are not here are 1, 3, 15, 45, 255, 765, 3825, 11475, 65535, 196605, 983025, ..., which are the values of iphi at powers of 2.

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

Cf. A091732, A362484, A362485.

Similar sequences: A005277, A005278, A347771, A362182.

Select[Range[120], Length[invIPhi[#]] == 0 &] (* using the function invIPhi from A362484 *)

A362485(a(n)) = 0.

cp's OEIS Frontend

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

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