A092843 a(n) = Sum_{k|n, k>1} phi(k-1), where phi() is the Euler phi function.

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, 12, 48, 8, 47, 21, 29, 20, 62, 12, 43, 23, 59, 16, 68, 12, 61, 33, 35, 22, 100, 18, 59, 29, 59, 24, 90, 24, 81, 31, 49, 28, 136, 16, 69, 45, 83, 38, 86, 20, 97, 43, 83, 24, 160, 24, 85

Offset: 1

Author

Leroy Quet, Nov 09 2004

Keywords

• nonn

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A069949.

Programs

Magma

f:= func< n | n eq 1 select 0 else EulerPhi(n-1) >;
A092843:= func< n | (&+[f(d): d in Divisors(n)]) >;
[A092843(n): n in [1..100]]; // G. C. Greubel, Jun 24 2024

Mathematica

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

PARI

a(n) = sumdiv(n, k, if (k>1, eulerphi(k-1))); \\ Michel Marcus, Jun 25 2024

SageMath

def A092843(n): return sum(euler_phi(k-1) for k in (1..n) if (k).divides(n))
[A092843(n) for n in range(1, 101)] # G. C. Greubel, Jun 24 2024

Formula

Conjecture: Sum_{k=1..n} a(k) ~ n^2/2. - Vaclav Kotesovec, Jun 25 2024

Extensions

More terms from Robert G. Wilson v, Nov 12 2004