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

3,3

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).

Links

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

Example

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.

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}]

Crossrefs

Cf. A000010, A215947.

Sequence in context: A169978 A068468 A200022 * A216851 A179290 A342014

Adjacent sequences: A216154 A216155 A216156 * A216158 A216159 A216160

Keyword

nonn

Author

Michel Lagneau, Sep 02 2012

Status

approved