A339312 Sum over all partitions of n of the GCD of the number of parts and the number of distinct parts.

0, 1, 2, 4, 6, 10, 17, 23, 33, 47, 71, 92, 129, 169, 235, 299, 408, 525, 691, 885, 1147, 1427, 1832, 2312, 2878, 3635, 4519, 5631, 7002, 8637, 10514, 13055, 15864, 19396, 23530, 28702, 34746, 42210, 50671, 61224, 73506, 88394, 105447, 126398, 150588, 179075

Offset: 0

Author

Alois P. Heinz, Dec 02 2020

Keywords

• nonn

Links

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

Crossrefs

Cf. A003989, A050873, A096541, A339006, A339011, A339394.

Programs

Maple

b:= proc(n, i, p, d) option remember; `if`(n=0, igcd(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, GCD[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 *)