A200792 Number of partitions of n such that the number of parts and the greatest part are not coprime.

0, 0, 1, 1, 3, 3, 7, 8, 12, 14, 24, 29, 43, 53, 72, 87, 119, 145, 196, 241, 314, 386, 505, 617, 786, 960, 1202, 1456, 1813, 2186, 2698, 3253, 3975, 4778, 5827, 6979, 8463, 10127, 12217, 14566, 17509, 20810, 24895, 29513, 35128, 41496, 49220, 57949, 68445

Offset

1,5

Links

Alois P. Heinz, Table of n, a(n) for n = 1..500

Example

a(5) = 3: [1,1,1,2], [1,1,3], [1,4].
a(6) = 3: [1,1,2,2], [1,2,3], [2,4].
a(7) = 7: [1,1,1,1,1,2], [1,2,2,2], [2,2,3], [1,3,3], [1,1,1,4], [3,4], [1,6].

Maple

b:= proc(n, j, t) option remember;
      add(b(n-i, i, t+1), i=j..iquo(n, 2))+
      `if`(igcd(t, n)>1, 1, 0)
    end:
a:= n-> b(n, 1, 1):
seq(a(n), n=1..60);

Mathematica

b[n_, j_, t_] := b[n, j, t] = Sum[b[n-i, i, t+1], {i, j, Quotient[n, 2]}] + If[GCD[t, n] > 1, 1, 0]; a[n_] := b[n, 1, 1]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Feb 06 2017, translated from Maple *)

Crossrefs

Cf. A199887.

Sequence in context: A021886 A178238 A255333 * A218567 A161416 A241637

Adjacent sequences: A200789 A200790 A200791 * A200793 A200794 A200795

Keyword

nonn

Author

Alois P. Heinz, Nov 22 2011

Status

approved