A025530 a(n) = (1/1 - 1/2 + ... + (-1)^(n-1)/n)*lcm{1..n}.

1, 1, 5, 7, 47, 37, 319, 533, 1879, 1627, 20417, 18107, 263111, 237371, 261395, 477745, 8842385, 8161705, 167324635, 155685007, 166770367, 156188887, 3825136961, 3602044091, 19081066231, 18051406831, 57128792093, 54260455193, 1653866633797

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• easy
• nice

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Index entries for sequences related to lcm's

Crossrefs

Cf. A058312, A058313, A003418, A033999.

Programs

Haskell

a025530 n = sum $ map (div (a003418 $ fromInteger n))
                      (zipWith (*) [1..n] a033999_list)
-- Reinhard Zumkeller, Dec 23 2011

Mathematica

nn=30;With[{fr=Accumulate[Table[1/(n (-1)^(n-1)),{n,nn}]]}, Table[fr[[n]] LCM@@ Range[n],{n,nn}]] (* Harvey P. Dale, Dec 27 2012 *)

PARI

a(n)=my(v=primes(primepi(n)),k=sqrtint(n),L=log(n+.5),t);t=prod(i=1,#v,if(v[i]>k,v[i],v[i]^(L\log(v[i]))));-sum(i=1,n,(-1)^i*t/i) \\ Charles R Greathouse IV, Dec 23 2011

PARI

s=1;v=vector(10^4,i,1);for(n=2,#v,t=n/gcd(s,n);s*=t;v[n]=v[n-1]*t-(-1)^n*s/n);v \\ Charles R Greathouse IV, Dec 23 2011