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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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified November 29 18:13 EST 2022. Contains 358431 sequences. (Running on oeis4.)