A159553 a(n) = Sum_{k=0..n} binomial(n,k) * gcd(n,k).

2, 6, 12, 28, 40, 144, 140, 536, 864, 2560, 2068, 12720, 8216, 45192, 78660, 182832, 131104, 933984, 524324, 3698240, 4890648, 13345816, 8388652, 67390464, 60129600, 225470544, 279938160, 1032462256, 536870968, 5018059200

Offset: 1

Author

Leroy Quet, Apr 14 2009

Keywords

• nonn

Comments

For the purpose of this sequence, gcd(n,0) = n, for all positive integers n.

a(n) is a multiple of n, for all nonnegative integers n.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..3317

Crossrefs

Cf. A159068, A159554.

Programs

Maple

A159553 := proc(n) add(binomial(n, k)*gcd(k, n), k=0..n) ; end: seq(A159553(n),n=1..40) ; # R. J. Mathar, Apr 29 2009

Mathematica

Table[Sum[Binomial[n, k] GCD[n, k], {k, 0, n}], {n, 30}] (* Michael De Vlieger, Oct 30 2017 *)

Formula

a(n) = A159068(n) + n.

a(n) = 2^n * Sum_{d|n} (phi(d)/d) * Sum_{k=1..d} (-1)^(k*n/d)*cos(k*Pi/d)^n.

Extensions

Extended by R. J. Mathar, Apr 29 2009

Ambiguous term a(0) removed by Max Alekseyev, Jan 09 2015