A200750 Number of partitions of n such that the number of parts and the greatest part are coprime.

1, 2, 2, 4, 4, 8, 8, 14, 18, 28, 32, 48, 58, 82, 104, 144, 178, 240, 294, 386, 478, 616, 750, 958, 1172, 1476, 1808, 2262, 2752, 3418, 4144, 5096, 6168, 7532, 9056, 10998, 13174, 15888, 18968, 22772, 27074, 32364, 38366, 45662, 54006, 64062, 75534, 89324

Offset: 1

Author

Alois P. Heinz, Nov 21 2011

Keywords

• nonn

Examples

			a(5) = 4: [1,1,1,1,1], [1,2,2], [2,3], [5].
a(6) = 8: [1,1,1,1,1,1], [1,1,1,1,2], [2,2,2], [1,1,1,3], [3,3], [1,1,4], [1,5], [6].
		

Links

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

Crossrefs

Cf. A199886.

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];
Array[a, 60] (* Jean-François Alcover, Dec 05 2020, after Alois P. Heinz *)