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.

1, 1, 2, 3, 6, 5, 12, 15, 20, 21, 30, 35, 60, 45, 56, 105, 210, 77, 420, 99, 220, 315, 840, 385, 924, 1155, 1540, 585, 2520, 364, 4620, 3465, 3640, 4620, 3432, 5005, 13860, 8190, 6160, 9009, 30030, 4290, 60060, 9945, 12376, 45045, 120120, 17017, 51480, 36036

Offset: 1

Author

Antti Karttunen, May 15 2013

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A225656, A225636, A225637, A225558.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, {1},
      `if`(i<1, {}, {seq(map(x->ilcm(x, `if`(j=0, 1, i)),
       b(n-i*j, i-1))[], j=0..n/i)}))
    end:
a:= n-> max(seq(ilcm(n, i), i=b(n$2)))/n:
seq(a(n), n=1..50);  # Alois P. Heinz, May 25 2013

Mathematica

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 *)

Scheme

(define (A225652 n) (/ (A225646 n) (max 1 n)))

Formula

a(n) = A225646(n)/n.