

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
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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_{dn} (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

Cf. A159068, A159554.
Sequence in context: A185961 A290674 A290419 * A327727 A222970 A112510
Adjacent sequences: A159550 A159551 A159552 * A159554 A159555 A159556


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



