

A238232


Composite numbers n such that the sum of numbers x<=n not coprime to n divides the sum of numbers y<=n coprime to n.


3



15, 35, 95, 119, 143, 209, 255, 287, 319, 323, 377, 527, 559, 779, 899, 923, 989, 1007, 1189, 1199, 1295, 1343, 1349, 1763, 1919, 2159, 2507, 2759, 2911, 3239, 3599, 3827, 4031, 4607, 5183, 5207, 5249, 5459, 5543, 6439, 6479, 6887, 7067, 7279, 7739, 8159, 8639
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Also numbers n such that n+1phi(n)  phi(n).
A203966 lists the numbers n such that the sum of numbers x<=n coprime to n divides the sum of numbers y<=n not coprime to n. This is equivalent to numbers n such that phi(n)  n+1. [suggested by Giovanni Resta]


LINKS



EXAMPLE

The numbers coprime to 15 are 1, 2, 4, 7, 8, 11, 13, 14 and their sum is 60. In fact 15*phi(15)/2 = 60.
The sum of the numbers from 1 to 15 is 15*(15+1)/2 = 120 and therefore the sum of the numbers not coprime to 15 is 120  60 = 60. At the end we have that 60/60 = 1.


MAPLE

with(numtheory); P:=proc(q) local i, n;
for n from 2 to q do if not isprime(n) then
if type(phi(n)/(n+1phi(n)), integer) then print(n);
fi; fi; od; end: P(10^6);


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



