OFFSET
1,4
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{d divides n} floor(d/2)*phi(n/d). a(p) = (p-1)/2 for an odd prime p. - Vladeta Jovovic, Dec 21 2004
a(n) = Sum_{i=1..floor(n/2)} gcd(n-i,i). - Wesley Ivan Hurt, Nov 12 2017
G.f.: Sum_{k>=1} phi(k)*x^(2*k)/((1 + x^k)*(1 - x^k)^2). - Ilya Gutkovskiy, Oct 24 2018
EXAMPLE
a(12) = gcd(1,11) + gcd(2,10) + gcd(3,9) + gcd(4,8) + gcd(5,7) + gcd(6,6) = 1 + 2 + 3 + 4 + 1 + 6 = 17;
a(13) = gcd(1,12) + gcd(2,11) + gcd(3,10) + gcd(4,9) + gcd(5,8) + gcd(6,7) = 1 + 1 + 1 + 1 + 1 + 1 = 6.
MAPLE
N:= 200: # to get a(1)..a(N)
A:= Vector(N):
for d from 1 to N do
c:= floor(d/2);
for n from d to N by d do
A[n]:= A[n]+c*numtheory:-phi(n/d)
od
od:
seq(A[i], i=1..N); # Robert Israel, May 11 2018
MATHEMATICA
Table[Sum[GCD[n - i, i], {i, Floor[n/2]}], {n, 100}] (* Wesley Ivan Hurt, Nov 12 2017 *)
PROG
(PARI) a(n) = sumdiv(n, d, (d\2)*eulerphi(n/d)); \\ Michel Marcus, May 11 2018
CROSSREFS
KEYWORD
AUTHOR
Reinhard Zumkeller, Feb 14 2002
STATUS
approved