%I #32 Oct 27 2023 21:50:23
%S 1,1,1,1,1,1,1,1,1,3,1,5,1,6,7,1,1,10,1,21,20,15,1,35,1,30,1,55,1,154,
%T 1,1,140,105,264,385,1,210,420,693,1,780,1,1365,1001,420,1,1155,1,462,
%U 3080,3465,1,770,6552,6435,5460,1260,1,17017,1,2310,12155
%N a(n) = (1/n) * lcm(p1,p2,...,pk) for such a partition of n that this formula produces an integer and maximizes this value among all such partitions [p1,p2,...,pk] of n.
%H Alois P. Heinz, <a href="/A225656/b225656.txt">Table of n, a(n) for n = 1..100</a> (terms n = 1..83 from Antti Karttunen)
%F a(n) = A225655(n)/n.
%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))[])/n:
%p seq(a(n), n=1..50); # _Alois P. Heinz_, May 25 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&]]/n; Table[a[n], {n, 1, 50}] (* _Jean-François Alcover_, Jul 29 2015, after _Alois P. Heinz_ *)
%o (Scheme): (define (A225656 n) (/ (A225655 n) (max 1 n)))
%Y Cf. A225652, A225636, A225657 (position of ones).
%K nonn
%O 1,10
%A _Antti Karttunen_, May 19 2013