A333297 - OEIS

%I #27 Nov 27 2020 07:06:23

%S 1,4,13,25,55,73,136,184,265,325,490,562,796,922,1102,1294,1702,1864,

%T 2377,2617,2995,3325,4084,4372,5122,5590,6319,6823,8041,8401,9796,

%U 10564,11554,12370,13630,14278,16276,17302,18706,19666,22126,22882,25591,26911,28531,30049,33292,34444,37531,39031

%N a(n) = Sum_{i=1..n, j=1..n, gcd(i,j)=1} i.

%H Alois P. Heinz, <a href="/A333297/b333297.txt">Table of n, a(n) for n = 1..10000</a>

%F From _Alois P. Heinz_, Mar 25 2020: (Start)

%F a(n) = a(n-1) + 3*n*phi(n)/2 for n > 1, a(n) = n for n <= 1.

%F a(n) = 1 + Sum_{k=2..n} 3*k*phi(k)/2. (End)

%F a(n) = a(n-1) + 3 * A023896(n) for n > 1. - _Hugo Pfoertner_, Mar 26 2020

%p Vi := proc(m,n) local a,i,j; a:=0;

%p for i from 1 to m do for j from 1 to n do

%p if igcd(i,j)=1 then a:=a+i; fi; od: od: a; end;

%p # the diagonal :

%p [seq(Vi(n,n),n=1..50)];

%p # second Maple program:

%p a:= proc(n) option remember; `if`(n<2, n,

%p       a(n-1) + 3*n*numtheory[phi](n)/2)

%p     end:

%p seq(a(n), n=1..50);  # _Alois P. Heinz_, Mar 25 2020

%t a[n_] := a[n] = If[n < 2, n, a[n - 1] + 3 n EulerPhi[n]/2];

%t Array[a, 50] (* _Jean-François Alcover_, Nov 27 2020, after _Alois P. Heinz_ *)

%o (PARI) a(n)={my(s=0);for(i=1,n,for(j=1,n,if(gcd(i,j)==1,s+=i)));s};

%o for(k=1,45,print1(a(k),", ")) \\ _Hugo Pfoertner_, Mar 25 2020

%Y Cf. A000010, A002618, A023896, A115004, A018805, A319087, A333295.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Mar 25 2020