A238232 - OEIS

%I #13 Feb 24 2014 04:21:37

%S 15,35,95,119,143,209,255,287,319,323,377,527,559,779,899,923,989,

%T 1007,1189,1199,1295,1343,1349,1763,1919,2159,2507,2759,2911,3239,

%U 3599,3827,4031,4607,5183,5207,5249,5459,5543,6439,6479,6887,7067,7279,7739,8159,8639

%N 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.

%C Also numbers n such that n+1-phi(n) | phi(n).

%C 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]

%H Paolo P. Lava, <a href="/A238232/b238232.txt">Table of n, a(n) for n = 1..1000</a>

%e 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.

%e 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.

%p with(numtheory);P:=proc(q) local i,n;

%p for n from 2 to q do if not isprime(n) then

%p if type(phi(n)/(n+1-phi(n)),integer) then print(n);

%p fi; fi; od; end: P(10^6);

%Y Cf. A061367, A050474, A070161, A142591, A203966.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Feb 21 2014