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 A072979 a(n) = sum_{k=1..n-1} gcd(k,n)a(k), a(1) = 1. 1
 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)
 OFFSET 1,3 LINKS _Reinhard Zumkeller_, Table of n, a(n) for n = 1..1000 EXAMPLE a(4) = gcd(1,4)a(1) + gcd(2,4)a(2) + gcd(3,4)a(3) = 1*1 + 2*1 + 1*2 = 5. MATHEMATICA f[n_] := f[n] = Sum[ GCD[k, n]*f[k], {k, 1, n - 1}]; f[1] = 1; Table[ f[n], {n, 1, 31} ] PROG (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 CROSSREFS Sequence in context: A136108 A026297 A109742 * A094600 A139796 A086586 Adjacent sequences:  A072976 A072977 A072978 * A072980 A072981 A072982 KEYWORD easy,nice,nonn AUTHOR Paul D. Hanna, Aug 20 2002 STATUS approved

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