%I #17 Jun 25 2024 04:02:19

%S 0,1,1,3,2,6,2,9,5,9,4,18,4,15,9,17,8,26,6,29,11,17,10,46,10,25,17,35,

%T 12,48,8,47,21,29,20,62,12,43,23,59,16,68,12,61,33,35,22,100,18,59,29,

%U 59,24,90,24,81,31,49,28,136,16,69,45,83,38,86,20,97,43,83,24,160,24,85

%N a(n) = Sum_{k|n, k>1} phi(k-1), where phi() is the Euler phi function.

%H G. C. Greubel, <a href="/A092843/b092843.txt">Table of n, a(n) for n = 1..10000</a>

%F Conjecture: Sum_{k=1..n} a(k) ~ n^2/2. - _Vaclav Kotesovec_, Jun 25 2024

%e a(6) = phi(2-1) + phi(3-1) + phi(6-1) = 1 + 1 + 4 = 6.

%t f[n_] := Block[{k = Drop[Divisors[n], 1]}, Plus @@ EulerPhi[k - 1]]; Table[ f[n], {n, 75}] (* _Robert G. Wilson v_, Nov 12 2004 *)

%o (Magma)

%o f:= func< n | n eq 1 select 0 else EulerPhi(n-1) >;

%o A092843:= func< n | (&+[f(d): d in Divisors(n)]) >;

%o [A092843(n): n in [1..100]]; // _G. C. Greubel_, Jun 24 2024

%o (SageMath)

%o def A092843(n): return sum(euler_phi(k-1) for k in (1..n) if (k).divides(n))

%o [A092843(n) for n in range(1, 101)] # _G. C. Greubel_, Jun 24 2024

%o (PARI) a(n) = sumdiv(n, k, if (k>1, eulerphi(k-1))); \\ _Michel Marcus_, Jun 25 2024

%Y Cf. A000010, A069949.

%K nonn

%O 1,4

%A _Leroy Quet_, Nov 09 2004

%E More terms from _Robert G. Wilson v_, Nov 12 2004