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%I #30 Oct 27 2023 21:50:43
%S 1,2,3,4,5,6,7,8,9,30,11,60,13,84,105,16,17,180,19,420,420,330,23,840,
%T 25,780,27,1540,29,4620,31,32,4620,3570,9240,13860,37,7980,16380,
%U 27720,41,32760,43,60060,45045,19320,47,55440,49,23100,157080,180180,53
%N a(n) = largest LCM of partitions of n divisible by n.
%C a(n) = lcm(p1,p2,...,pk) for that partition of n for which the LCM is a multiple of n, and which maximizes this value among all such partitions [p1,p2,...,pk] of n.
%H Alois P. Heinz, <a href="/A225655/b225655.txt">Table of n, a(n) for n = 1..100</a> (terms n = 0..83 from Antti Karttunen)
%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>
%p b:= proc(n, i) option remember; `if`(n=0, {1},
%p `if`(i<1, {}, {seq(map(x->ilcm(x, `if`(j=0, 1, i)),
%p b(n-i*j, i-1))[], j=0..n/i)}))
%p end:
%p a:= n-> max(select(x-> irem(x, n)=0, b(n$2))[]):
%p seq(a(n), n=1..50); # _Alois P. Heinz_, May 26 2013
%t b[n_, i_] := b[n, i] = If[n==0, {1}, If[i<1, {}, Union @ Flatten @ Table[ Map[ Function[{x}, LCM[x, If[j==0, 1, i]]], b[n-i*j, i-1]], {j, 0, n/i}]]]; a[n_] := Max[Select[b[n, n], Mod[#, n]==0&]]; Table[a[n], {n, 1, 50}] (* _Jean-François Alcover_, Jul 29 2015, after _Alois P. Heinz_ *)
%Y For all n, a(A225651(n)) = A000793(A225651(n)).
%Y Cf. A225646, A225656, A225652.
%Y A225657 lists the values of n for which a(n) = n.
%K nonn
%O 1,2
%A _Antti Karttunen_, May 19 2013
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