A072979 a(n) = Sum_{k=1..n-1} gcd(k,n)*a(k), a(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

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