A190940 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).

0, 1, 2, 2, 6, 4, 12, 8, 16, 18, 48, 32, 96, 72, 64, 48, 240, 128, 480, 288, 320, 384, 960, 512

Offset

1,3

Links

Table of n, a(n) for n=1..24.

Formula

Conjecture: a(n) = A000005(A002944(n)), for n >= 2. - Ridouane Oudra, Aug 24 2019

Example

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.

Maple

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

Mathematica

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 *)

Crossrefs

Cf. A101207.

Sequence in context: A054585 A278236 A278226 * A336869 A046203 A321451

Adjacent sequences: A190937 A190938 A190939 * A190941 A190942 A190943

Keyword

nonn,more

Author

Naohiro Nomoto, May 24 2011

Extensions

a(12)-a(20) from R. J. Mathar, Jun 02 2011

a(21)-a(24) from Alois P. Heinz, Nov 03 2011

Status

approved