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A333297 a(n) = Sum_{i=1..n, j=1..n, gcd(i,j)=1} i.

%I A333297 #31 Dec 01 2024 03:41:18
%S A333297 1,4,13,25,55,73,136,184,265,325,490,562,796,922,1102,1294,1702,1864,
%T A333297 2377,2617,2995,3325,4084,4372,5122,5590,6319,6823,8041,8401,9796,
%U A333297 10564,11554,12370,13630,14278,16276,17302,18706,19666,22126,22882,25591,26911,28531,30049,33292,34444,37531,39031
%N A333297 a(n) = Sum_{i=1..n, j=1..n, gcd(i,j)=1} i.
%H A333297 Alois P. Heinz, <a href="/A333297/b333297.txt">Table of n, a(n) for n = 1..10000</a>
%F A333297 From _Alois P. Heinz_, Mar 25 2020: (Start)
%F A333297 a(n) = a(n-1) + 3*n*phi(n)/2 for n > 1, a(n) = n for n <= 1.
%F A333297 a(n) = 1 + Sum_{k=2..n} 3*k*phi(k)/2. (End)
%F A333297 a(n) = a(n-1) + 3 * A023896(n) for n > 1. - _Hugo Pfoertner_, Mar 26 2020
%F A333297 a(n) ~ (3/Pi^2) * n^3. - _Amiram Eldar_, Dec 01 2024
%p A333297 Vi := proc(m,n) local a,i,j; a:=0;
%p A333297 for i from 1 to m do for j from 1 to n do
%p A333297 if igcd(i,j)=1 then a:=a+i; fi; od: od: a; end;
%p A333297 # the diagonal :
%p A333297 [seq(Vi(n,n),n=1..50)];
%p A333297 # second Maple program:
%p A333297 a:= proc(n) option remember; `if`(n<2, n,
%p A333297       a(n-1) + 3*n*numtheory[phi](n)/2)
%p A333297     end:
%p A333297 seq(a(n), n=1..50);  # _Alois P. Heinz_, Mar 25 2020
%t A333297 a[n_] := a[n] = If[n < 2, n, a[n - 1] + 3 n EulerPhi[n]/2];
%t A333297 Array[a, 50] (* _Jean-François Alcover_, Nov 27 2020, after _Alois P. Heinz_ *)
%o A333297 (PARI) a(n)={my(s=0);for(i=1,n,for(j=1,n,if(gcd(i,j)==1,s+=i)));s};
%o A333297 for(k=1,45,print1(a(k),", ")) \\ _Hugo Pfoertner_, Mar 25 2020
%Y A333297 Cf. A000010, A002618, A023896, A115004, A018805, A319087, A333295.
%K A333297 nonn
%O A333297 1,2
%A A333297 _N. J. A. Sloane_, Mar 25 2020