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

1,2

Links

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

Example

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].

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 *)

Crossrefs

Cf. A199886.

Sequence in context: A205478 A262966 A034397 * A344607 A325722 A279818

Adjacent sequences: A200747 A200748 A200749 * A200751 A200752 A200753

Keyword

nonn

Author

Alois P. Heinz, Nov 21 2011

Status

approved