A216157 Difference between the sum of the even divisors and the sum of the odd divisors of phi(n).

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, 13, 24, 29, 30, 29, 52, 20, 65, 13, 52, 29, 78, 20, 32, 30, 52, 12, 24, 29, 32, 30, 61, 52, 70, 13, 78, 52, 65, 40, 30, 29, 120, 24, 65, 61, 116, 30, 48, 61, 60, 52

Offset: 3

Author

Michel Lagneau, Sep 02 2012

Keywords

• nonn

Comments

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

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

Examples

			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.
		

Links

• Michel Lagneau, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A000010, A215947.

Programs

Maple

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:

Mathematica

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