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A225652 a(n) = (1/n) * lcm(n,p1,p2,...,pk) for that partition of n which maximizes this value among all partitions [p1,p2,...,pk] of n.

%I A225652 #25 Mar 05 2025 13:43:19
%S A225652 1,1,2,3,6,5,12,15,20,21,30,35,60,45,56,105,210,77,420,99,220,315,840,
%T A225652 385,924,1155,1540,585,2520,364,4620,3465,3640,4620,3432,5005,13860,
%U A225652 8190,6160,9009,30030,4290,60060,9945,12376,45045,120120,17017,51480,36036
%N A225652 a(n) = (1/n) * lcm(n,p1,p2,...,pk) for that partition of n which maximizes this value among all partitions [p1,p2,...,pk] of n.
%H A225652 Alois P. Heinz, <a href="/A225652/b225652.txt">Table of n, a(n) for n = 1..100</a>
%F A225652 a(n) = A225646(n)/n.
%p A225652 b:= proc(n, i) option remember; `if`(n=0, {1},
%p A225652       `if`(i<1, {}, {seq(map(x->ilcm(x, `if`(j=0, 1, i)),
%p A225652        b(n-i*j, i-1))[], j=0..n/i)}))
%p A225652     end:
%p A225652 a:= n-> max(seq(ilcm(n, i), i=b(n$2)))/n:
%p A225652 seq(a(n), n=1..50);  # _Alois P. Heinz_, May 25 2013
%t A225652 b[n_, i_] := b[n, i] = If[n==0, {1}, If[i<1, {}, Table[Map[Function[{x}, LCM[x, If[j==0, 1, i]]], b[n-i*j, i-1]], {j, 0, n/i}]]]; a[n_] := Max[Table[LCM[n, i], {i, b[n, n]}]]/n; Table[Print["a(", n, ") = ", an = a[n]]; an, {n, 1, 50}] (* _Jean-François Alcover_, Jul 29 2015, after _Alois P. Heinz_ *)
%o A225652 (Scheme) (define (A225652 n) (/ (A225646 n) (max 1 n)))
%Y A225652 Cf. A225656, A225636, A225637, A225558.
%K A225652 nonn
%O A225652 1,3
%A A225652 _Antti Karttunen_, May 15 2013