A069949 a(n) = Sum_{d|n} phi(d+1).

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, 47, 9, 61, 17, 49, 23, 33, 19, 85, 19, 35, 25, 77, 13, 75, 21, 57, 39, 57, 17, 111, 25, 59, 33, 83, 19, 85, 31, 89, 39, 69, 17, 149, 31, 55, 53, 97, 29, 119, 33, 81, 35, 109, 25, 183

Offset: 1

Author

Vladeta Jovovic, May 04 2002

Keywords

• nonn

Links

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

Crossrefs

Cf. A000010, A092843.

Programs

Magma

A069949:= func< n | (&+[EulerPhi(d+1): d in Divisors(n)]) >;
[A069949(n): n in [1..100]]; // G. C. Greubel, Jun 24 2024

Mathematica

A069949[n_]:= DivisorSum[n, EulerPhi[#+1] &];
Table[A069949[n], {n,100}] (* G. C. Greubel, Jun 24 2024 *)

PARI

a(n)=sumdiv(n, d, eulerphi(d+1) );  /* Joerg Arndt, Sep 30 2012 */

SageMath

def A069949(n): return sum(euler_phi(k+1) for k in (1..n) if (k).divides(n))
[A069949(n) for n in range(1,101)] # G. C. Greubel, Jun 24 2024

Formula

a(n) = Sum_{k=1..n} phi(gcd(n,k) + 1)/phi(n/gcd(n,k)). - Richard L. Ollerton, May 09 2021