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Search: id:A159068
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| A159068 |
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a(n) = sum{k=1 to n} binomial(n,k) * GCD(k,n). |
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+0
5
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| 1, 4, 9, 24, 35, 138, 133, 528, 855, 2550, 2057, 12708, 8203, 45178, 78645, 182816, 131087, 933966, 524305, 3698220, 4890627, 13345794, 8388629, 67390440, 60129575, 225470518, 279938133, 1032462228, 536870939, 5018059170
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OFFSET
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1,2
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COMMENT
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Each term of the sum a(n) is divisible by n, so a(n) is a multiple of n for all positive integers n.
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EXAMPLE
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Row 6 of Pascal's triangle is: 1,6,15,20,15,6,1. The greatest common divisors of n and each integer from 1 to 6 are: GCD(1,6)=1, GCD(2,6)=2, GCD(3,6)=3, GCD(4,6)=2, GCD(5,6)=1, and GCD(6,6)=6. So a(6) = 6*1 + 15*2 + 20*3 + 15*2 + 6*1 + 1*6 = 138. Note that each term of the sum is a multiple of 6, so 138 is a multiple of 6.
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MAPLE
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A159068 := proc(n) add(binomial(n, k)*gcd(k, n), k=1..n) ; end: seq(A159068(n), n=1..80) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 06 2009]
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CROSSREFS
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A159069
Sequence in context: A067801 A062775 A046422 this_sequence A158141 A056575 A056032
Adjacent sequences: A159065 A159066 A159067 this_sequence A159069 A159070 A159071
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Apr 04 2009
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EXTENSIONS
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Extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 06 2009
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