cp's OEIS Frontend

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.

%I A238232 #13 Feb 24 2014 04:21:37
%S A238232 15,35,95,119,143,209,255,287,319,323,377,527,559,779,899,923,989,
%T A238232 1007,1189,1199,1295,1343,1349,1763,1919,2159,2507,2759,2911,3239,
%U A238232 3599,3827,4031,4607,5183,5207,5249,5459,5543,6439,6479,6887,7067,7279,7739,8159,8639
%N 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.
%C A238232 Also numbers n such that n+1-phi(n) | phi(n).
%C A238232 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 A238232 Paolo P. Lava, <a href="/A238232/b238232.txt">Table of n, a(n) for n = 1..1000</a>
%e A238232 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 A238232 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 A238232 with(numtheory);P:=proc(q) local i,n;
%p A238232 for n from 2 to q do if not isprime(n) then
%p A238232 if type(phi(n)/(n+1-phi(n)),integer) then print(n);
%p A238232 fi; fi; od; end: P(10^6);
%Y A238232 Cf. A061367, A050474, A070161, A142591, A203966.
%K A238232 nonn
%O A238232 1,1
%A A238232 _Paolo P. Lava_, Feb 21 2014