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A072979
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a(n) = sum_{k=1..n-1} gcd(k,n)a(k), a(1) = 1.
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1
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1, 1, 2, 5, 9, 28, 46, 136, 288, 722, 1238, 4342, 6818, 19146, 45026, 111698, 189506, 624930, 1003942, 3187170, 6659438, 15815050, 27669542, 98100426, 166371218, 437756198, 972187194, 2528368182, 4258122302, 14644463794, 23160708398
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 1..1000
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EXAMPLE
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a(4) = gcd(1,4)a(1) + gcd(2,4)a(2) + gcd(3,4)a(3) = 1*1 + 2*1 + 1*2 = 5.
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MATHEMATICA
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f[n_] := f[n] = Sum[ GCD[k, n]*f[k], {k, 1, n - 1}]; f[1] = 1; Table[ f[n], {n, 1, 31} ]
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PROG
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(Haskell)
a072979 n = a072979_list !! (n-1)
a072979_list = 1 : f 2 [1] where
f z xs = y : f (z + 1) (y : xs) where
y = sum $ zipWith (*) xs (map (gcd z) [z-1, z-2 ..])
-- Reinhard Zumkeller, Feb 13 2012
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CROSSREFS
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Sequence in context: A136108 A026297 A109742 * A094600 A139796 A086586
Adjacent sequences: A072976 A072977 A072978 * A072980 A072981 A072982
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Paul D. Hanna, Aug 20 2002
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STATUS
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approved
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