

A111356


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


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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[ # ]]] &] (*Chandler*)


CROSSREFS

Cf. A045763.
Sequence in context: A303313 A257642 A066867 * A295692 A033267 A186402
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



