login
A339394
Sum over all partitions of n of the LCM of the number of parts and the number of distinct parts.
2
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Dec 02 2020
STATUS
approved