A339394 Sum over all partitions of n of the LCM of the number of parts and the number of distinct parts.

0, 1, 3, 6, 15, 26, 43, 81, 138, 218, 320, 514, 751, 1131, 1570, 2319, 3159, 4457, 6077, 8344, 11224, 15337, 20297, 26908, 35773, 46434, 60711, 78433, 100987, 129222, 166590, 209719, 267120, 335842, 423341, 527739, 659974, 816805, 1015990, 1251686, 1543864

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Maple

b:= proc(n, i, p, d) option remember; `if`(n=0, ilcm(p, d),
      add(b(n-i*j, i-1, p+j, d+signum(j)), j=`if`(i>1, 0..n/i, n)))
    end:
a:= n-> b(n$2, 0$2):
seq(a(n), n=0..50);

Mathematica

b[n_, i_, p_, d_] := b[n, i, p, d] = If[n == 0, LCM[p, d],
     Sum[b[n - i*j, i - 1, p + j, d + Sign[j]],
     {j, If[i > 1, Range[0, n/i], {n}]}]];
a[n_] := b[n, n, 0, 0];
a /@ Range[0, 50] (* Jean-François Alcover, Mar 09 2021, after Alois P. Heinz *)

Crossrefs

Cf. A003990, A051173, A339312.

Sequence in context: A216304 A020991 A079825 * A327067 A252745 A282662

Adjacent sequences: A339391 A339392 A339393 * A339395 A339396 A339397

Keyword

nonn

Author

Alois P. Heinz, Dec 02 2020

Status

approved