A093431 a(n) = Sum_{k=1..n} (lcm(n,n-1,...,n-k+2,n-k+1)/lcm(1,2,...,k)).

1, 3, 7, 13, 31, 38, 113, 165, 265, 420, 1607, 1004, 3979, 6893, 4205, 8665, 40903, 49558, 315477, 162320, 79179, 269877, 1647123, 937552, 1810091, 8445653, 7791355, 3978237, 33071543, 19578860, 283536169, 327438713, 117635955, 742042966, 154748983, 88779588

Offset: 1

Author

Amarnath Murthy, Mar 31 2004

Keywords

• nonn

Comments

The following sequences all appear to have the same parity: A003071, A029886, A061297, A092524, A093431, A102393, A104258, A122248, A128975. - Jeremy Gardiner, Dec 28 2008

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..4546

Crossrefs

Cf. A093430, A093432, A093433.

Row sums of A093430.

Programs

Maple

a:= n-> add(ilcm(seq(i,i=n-k+1..n))/ilcm(seq(j,j=1..k)),k=1..n): seq(a(n),n=1..40); # Emeric Deutsch, Jan 30 2006
# second Maple program:
b:= proc(n) option remember; `if`(n=1, 1, ilcm(b(n-1), n)) end:
a:= proc(n) option remember; local k, r, s; r, s:= 0, 1;
      for k to n do s:= ilcm(s,n-k+1); r:= r+s/b(k) od; r
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, Mar 17 2018

Mathematica

Table[Sum[(LCM@@(n-Range[0,k-1])/LCM@@Range[k]),{k,n}],{n,33}] (* Jayanta Basu, May 22 2013 *)

Extensions

Corrected and extended by Emeric Deutsch, Jan 30 2006