A124440 a(n) = Sum_{n/2<=k<=n, gcd(k,n)=1} k.
1, 1, 2, 3, 7, 5, 15, 12, 20, 16, 40, 18, 57, 33, 46, 48, 100, 41, 126, 60, 96, 85, 187, 72, 187, 120, 182, 126, 301, 88, 345, 192, 250, 208, 318, 162, 495, 261, 354, 240, 610, 186, 672, 330, 406, 385, 805, 288, 771, 376, 616, 468, 1027, 365, 830, 504, 774, 616, 1276
Offset: 1
Keywords
Examples
The integers which are >= 10/2 and are <= 10 and which are coprime to 10 are 7 and 9. So a(10) = 7 + 9 = 16.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
-
Maple
N:= 100: # for a(1)..a(N) G:= add(numtheory:-mobius(n)*n*x^(2*n)/((1-x^n)*(1-x^(2*n))^2), n=1..N/2): S:= series(G, x, N+1): A66840:= [seq(coeff(S, x, j), j=1..N)]: f:= proc(n) n*numtheory:-phi(n)/2 - A66840[n] end proc: f(1):= 1: f(2):= 1: map(f, [$1..N]); # Robert Israel, Feb 02 2021
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Mathematica
a[n_] := Plus @@ Select[Range[Ceiling[n/2], n], GCD[ #, n] == 1 &];Table[a[n], {n, 60}] (* Ray Chandler, Nov 12 2006 *) -
PARI
a(n) = sum(k=ceil(n/2), n, if (gcd(n, k)==1, k)); \\ Michel Marcus, Feb 03 2021
Formula
For n > 2, a(n) = phi(n)*n/2 - A066840(n).
Extensions
Extended by Ray Chandler, Nov 12 2006