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A190940
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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).
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1
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0, 1, 2, 2, 6, 4, 12, 8, 16, 18, 48, 32, 96, 72, 64, 48, 240, 128, 480, 288, 320, 384, 960, 512
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OFFSET
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1,3
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LINKS
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FORMULA
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EXAMPLE
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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.
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MAPLE
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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:
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
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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