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

%I A093431 #20 Mar 17 2018 21:14:24
%S A093431 1,3,7,13,31,38,113,165,265,420,1607,1004,3979,6893,4205,8665,40903,
%T A093431 49558,315477,162320,79179,269877,1647123,937552,1810091,8445653,
%U A093431 7791355,3978237,33071543,19578860,283536169,327438713,117635955,742042966,154748983,88779588
%N A093431 a(n) = Sum_{k=1..n} (lcm(n,n-1,...,n-k+2,n-k+1)/lcm(1,2,...,k)).
%C A093431 The following sequences all appear to have the same parity: A003071, A029886, A061297, A092524, A093431, A102393, A104258, A122248, A128975. - _Jeremy Gardiner_, Dec 28 2008
%H A093431 Alois P. Heinz, <a href="/A093431/b093431.txt">Table of n, a(n) for n = 1..4546</a>
%p A093431 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
%p A093431 # second Maple program:
%p A093431 b:= proc(n) option remember; `if`(n=1, 1, ilcm(b(n-1), n)) end:
%p A093431 a:= proc(n) option remember; local k, r, s; r, s:= 0, 1;
%p A093431       for k to n do s:= ilcm(s,n-k+1); r:= r+s/b(k) od; r
%p A093431     end:
%p A093431 seq(a(n), n=0..40);  # _Alois P. Heinz_, Mar 17 2018
%t A093431 Table[Sum[(LCM@@(n-Range[0,k-1])/LCM@@Range[k]),{k,n}],{n,33}] (* _Jayanta Basu_, May 22 2013 *)
%Y A093431 Cf. A093430, A093432, A093433.
%Y A093431 Row sums of A093430.
%K A093431 nonn
%O A093431 1,2
%A A093431 _Amarnath Murthy_, Mar 31 2004
%E A093431 Corrected and extended by _Emeric Deutsch_, Jan 30 2006