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A159553
a(n) = Sum_{k=0..n} binomial(n,k) * gcd(n,k).
3
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
1,1
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
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
Sequence in context: A185961 A290674 A290419 * A327727 A222970 A112510
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