OFFSET
1,1
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
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Apr 14 2009
EXTENSIONS
Extended by R. J. Mathar, Apr 29 2009
Ambiguous term a(0) removed by Max Alekseyev, Jan 09 2015
STATUS
approved