A225656 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.

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, 1, 1, 140, 105, 264, 385, 1, 210, 420, 693, 1, 780, 1, 1365, 1001, 420, 1, 1155, 1, 462, 3080, 3465, 1, 770, 6552, 6435, 5460, 1260, 1, 17017, 1, 2310, 12155

Offset: 1

Author

Antti Karttunen, May 19 2013

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..100 (terms n = 1..83 from Antti Karttunen)

Crossrefs

Cf. A225652, A225636, A225657 (position of ones).

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(select(x-> irem(x, n)=0, 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, {}, 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 *)

Scheme

(define (A225656 n) (/ (A225655 n) (max 1 n)))

Formula

a(n) = A225655(n)/n.