A111356 Numbers n such that the number of numbers "unrelated to n" is itself unrelated to n.

21, 24, 27, 36, 39, 57, 60, 64, 66, 75, 77, 84, 90, 93, 95, 100, 102, 105, 111, 129, 130, 132, 138, 144, 145, 150, 160, 162, 165, 168, 174, 175, 180, 183, 196, 201, 204, 210, 216, 219, 221, 230, 237, 246, 255, 256, 270, 275, 276, 282, 291, 295, 297, 309, 312

Offset

1,1

Links

Table of n, a(n) for n=1..55.

Formula

{a(n)} = {n: A045763(n) is not [a divisor of n] and is not [relatively prime to n] and is not 0}. {a(n)} = {n: n + 1 - d(n) - phi(n) is not [a divisor of n] and is not [relatively prime to n]}. where d is the number of divisors of n and phi is Euler's totient function. I am defining 0 to be not unrelated to n.

Example

The first value to be neither 0 (excluded from definition) nor 1 (always a divisor of n) is 10, for which A045763(10) = 3; but 3 is relatively prime to 10, hence not unrelated to 10, so 10 is not in this sequence. The second value to be neither 0 (excluded from definition) nor 1 (always a divisor of n) is 12, for which A045763(12) = 3; but 3 is a divisor of 12, hence not unrelated to 12, so 12 is not in this sequence.
a(1) = 21 because A045763(21) = 6, which is unrelated to 21 (shares the divisor 3).
a(2) = 24 because A045763(24) = 9, which is unrelated to 24 (shares the divisor 3).

Mathematica

u[n_] := Select[Range[n - 1], Mod[n, # ] > 0 && GCD[ #, n] > 1 &]; Select[Range[312], MemberQ[u[ # ], Length[u[ # ]]] &] (* Ray Chandler, Nov 09 2005 *)

Crossrefs

Cf. A045763.

Sequence in context: A257642 A332922 A066867 * A344806 A295692 A033267

Adjacent sequences: A111353 A111354 A111355 * A111357 A111358 A111359

Keyword

easy,nonn

Author

Jonathan Vos Post, Nov 06 2005

Extensions

Corrected and extended by Ray Chandler and Robert G. Wilson v, Nov 09 2005

Status

approved