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

0,3

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, 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 *)

Crossrefs

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

Sequence in context: A048833 A204656 A070689 * A091611 A107742 A228779

Adjacent sequences: A339309 A339310 A339311 * A339313 A339314 A339315

Keyword

nonn

Author

Alois P. Heinz, Dec 02 2020

Status

approved