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%I #23 Aug 25 2019 02:10:57
%S 0,1,2,2,6,4,12,8,16,18,48,32,96,72,64,48,240,128,480,288,320,384,960,
%T 512
%N Consider all compositions of n = a+b+c+..., as 2 or more positive integers a,b,c,... > 0. a(n) is the number of distinct values taken by lcm(a, a+b, a+b+c, ..., n).
%F Conjecture: a(n) = A000005(A002944(n)), for n >= 2. - _Ridouane Oudra_, Aug 24 2019
%e Examples: for n=3 the a(3) = 2 distinct values are 3, 6. The compositions are 1+2, 2+1, and 1+1+1. The values of the lcm are lcm(1,1+2)=3, lcm(2,2+1)=6, and lcm(1,1+1,1+1+1)=6.
%p Lpsum := proc(L) local ps,k ; ps := [op(1,L)] ; for i from 2 to nops(L) do ps := [op(ps), op(-1,ps)+op(i,L)] ; end do: ps ; end proc:
%p A190940 := proc(n) local lc,k,c ; lc := {} ; for k from 2 to n do for c in combinat[composition](n,k) do lc := lc union { ilcm( op(Lpsum(c))) }; end do: end do: nops(lc) ; end proc: # _R. J. Mathar_, Jun 02 2011
%t a[n_] := LCM @@@ (Accumulate /@ (Permutations /@ Rest[IntegerPartitions[n]] // Flatten[#, 1]&)) // Union // Length; Table[Print[an = a[n]]; an, {n, 1, 24}] (* _Jean-François Alcover_, Feb 27 2014 *)
%Y Cf. A101207.
%K nonn,more
%O 1,3
%A _Naohiro Nomoto_, May 24 2011
%E a(12)-a(20) from _R. J. Mathar_, Jun 02 2011
%E a(21)-a(24) from _Alois P. Heinz_, Nov 03 2011
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