A014454 - OEIS

%I #14 Nov 11 2013 14:09:15

%S 0,1,2,5,6,21,22,73,210,1693,1694,2097,2098,12997,21468,174169,174170,

%T 1986237,1986238,10178833,16875654,246551437,246551438,2032266537,

%U 3767596738,45445808989,260705796192,2932954933753,2932954933754,5496591783573,5496591783574

%N Sum_{1<=k<n} gcd(k!,n!/k!).

%H Reinhard Zumkeller, <a href="/A014454/b014454.txt">Table of n, a(n) for n = 1..500</a>

%e a(5) = gcd(1!,5!)+gcd(2!,3*4*5)+gcd(3!,4*5)+gcd(4!,5)=1+2+2+1 = 6.

%o (PARI) a(n) = sum(k=1, n-1, gcd(k!, n!/k!)); \\ _Michel Marcus_, Aug 04 2013

%o (Haskell)

%o a014454 n = sum $ zipWith gcd kfs $ map (div nf) kfs

%o    where (nf:kfs) = reverse $ a166350_row n

%o -- _Reinhard Zumkeller_, Nov 11 2013

%Y Cf. A000142.

%Y Cf. A166350.

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, Feb 12 2002