A069949 - OEIS

%I #17 Jun 25 2024 02:03:06

%S 1,3,3,7,3,11,5,13,7,15,5,27,7,15,13,29,7,33,9,31,17,29,9,53,15,27,19,

%T 47,9,61,17,49,23,33,19,85,19,35,25,77,13,75,21,57,39,57,17,111,25,59,

%U 33,83,19,85,31,89,39,69,17,149,31,55,53,97,29,119,33,81,35,109,25,183

%N a(n) = Sum_{d|n} phi(d+1).

%H G. C. Greubel, <a href="/A069949/b069949.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = Sum_{k=1..n} phi(gcd(n,k) + 1)/phi(n/gcd(n,k)). - _Richard L. Ollerton_, May 09 2021

%t A069949[n_]:= DivisorSum[n, EulerPhi[#+1] &];

%t Table[A069949[n], {n,100}] (* _G. C. Greubel_, Jun 24 2024 *)

%o (PARI) a(n)=sumdiv(n, d, eulerphi(d+1) );  /* _Joerg Arndt_, Sep 30 2012 */

%o (Magma)

%o A069949:= func< n | (&+[EulerPhi(d+1): d in Divisors(n)]) >;

%o [A069949(n): n in [1..100]]; // _G. C. Greubel_, Jun 24 2024

%o (SageMath)

%o def A069949(n): return sum(euler_phi(k+1) for k in (1..n) if (k).divides(n))

%o [A069949(n) for n in range(1,101)] # _G. C. Greubel_, Jun 24 2024

%Y Cf. A000010, A092843.

%K nonn

%O 1,2

%A _Vladeta Jovovic_, May 04 2002