A083245 - OEIS

%I #15 Jul 30 2017 12:01:44

%S 1,2,3,4,5,4,7,6,7,4,11,6,13,4,7,8,17,4,19,6,9,4,23,6,19,4,15,6,29,0,

%T 31,10,13,4,19,4,37,4,15,6,41,-4,43,6,13,4,47,2,39,0,19,6,53,-4,31,6,

%U 21,4,59,-6,61,4,19,12,37,-12,67,6,25,-8,71,-2,73,4,15,6,49,-16,79,2,35,4,83,-14,49,4,31,6,89,-20,59,6,33,4,55,-10,97,-4

%N Difference between numbers of related and numbers of unrelated numbers belonging to n: a(n) = A073757(n)-A045763(n) = (n-u(n))-u(n) = n-2*A045763(n) = 2*A073757(n)-n.

%C There are only 2 cases [n=30, n=50] below 10^7 such that a(n) = 0.

%C No other zeros found up to 10^9. - _Michel Marcus_, Jul 30 2017

%H Michel Marcus, <a href="/A083245/b083245.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 2(A000005(n)+A000010(n)-1)-n.

%e n=37, d=2,r=36,u=0, a(37)=2+36-1-0=37>0; primes are fixed points.

%e n=42, d=8,r=12,u=23,a(42)=8+12-1-23=-4<0, terms of A083244;

%e n=30, d=8,r=8,u=15, a(30)=0;

%e n=50, d=6,r=20,u=25,a(50)=0.

%t Table[2*(DivisorSigma[0, w]+EulerPhi[w]-1)-w, {w, 1, 1000}]

%o (PARI) a(n) = 2*(numdiv(n)+eulerphi(n)-1) - n; \\ _Michel Marcus_, Jul 30 2017

%Y Cf. A000005, A000010, A045763, A073757, A083243, A083244, A083246, A020488.

%K sign

%O 1,2

%A _Labos Elemer_, May 07 2003