A216157 - OEIS

%I #7 Sep 03 2012 14:34:00

%S 1,1,5,1,4,5,4,5,6,5,20,4,13,13,29,4,13,13,20,6,12,13,30,20,13,20,40,

%T 13,24,29,30,29,52,20,65,13,52,29,78,20,32,30,52,12,24,29,32,30,61,52,

%U 70,13,78,52,65,40,30,29,120,24,65,61,116,30,48,61,60,52

%N Difference between the sum of the even divisors and the sum of the odd divisors of phi(n).

%C phi(n) : A000010 is the Euler totient function, and even for n > 2.

%C If n prime, phi(n) = n-1 and a(n) = a((n-1)/2).

%H Michel Lagneau, <a href="/A216157/b216157.txt">Table of n, a(n) for n = 3..10000</a>

%e a(13) = 20 because the divisors of phi(13) = 12 are {1, 2, 3, 4, 6, 12} and (12 + 6 + 4 +2) - (3 + 1) = 20.

%p with(numtheory):for n from 3 to 100 do:x:=divisors(phi(n)):n1:=nops(x):s0:=0:s1:=0:for m from 1 to n1 do: if irem(x[m],2)=0 then s0:=s0+x[m]:else s1:=s1+x[m]:fi:od:if s0>s1  then printf(`%d, `,s0-s1):else fi:od:

%t Table[Total[Select[Divisors[EulerPhi[n]], EvenQ[#]&]]-Total[Select[Divisors[EulerPhi[n]], OddQ[#]&]], {n,3,80}]

%Y Cf. A000010, A215947.

%K nonn

%O 3,3

%A _Michel Lagneau_, Sep 02 2012