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

Author

Alois P. Heinz, Nov 22 2011

Keywords

• nonn

Examples

			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].
		

Links

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

Crossrefs

Cf. A199887.

Programs

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 *)