A111356 - OEIS

%I #8 Oct 11 2019 16:52:26

%S 21,24,27,36,39,57,60,64,66,75,77,84,90,93,95,100,102,105,111,129,130,

%T 132,138,144,145,150,160,162,165,168,174,175,180,183,196,201,204,210,

%U 216,219,221,230,237,246,255,256,270,275,276,282,291,295,297,309,312

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

%F {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.

%e 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.

%e a(1) = 21 because A045763(21) = 6, which is unrelated to 21 (shares the divisor 3).

%e a(2) = 24 because A045763(24) = 9, which is unrelated to 24 (shares the divisor 3).

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

%Y Cf. A045763.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Nov 06 2005

%E Corrected and extended by _Ray Chandler_ and _Robert G. Wilson v_, Nov 09 2005