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

Author

Jonathan Vos Post, Nov 06 2005

Keywords

• easy
• nonn

Examples

			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).
		

Crossrefs

Cf. A045763.

Programs

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 *)

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.

Extensions

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