A201218 Number of partitions of n such that the number of parts and the largest part and the smallest part are pairwise coprime.

1, 1, 1, 3, 2, 5, 6, 12, 13, 22, 25, 40, 47, 69, 85, 126, 148, 204, 249, 330, 404, 531, 647, 835, 1022, 1300, 1591, 2006, 2432, 3029, 3678, 4541, 5477, 6711, 8056, 9805, 11735, 14178, 16918, 20356, 24195, 28963, 34372, 40978, 48486, 57626, 68001, 80540, 94826

Offset

1,4

Links

Alois P. Heinz, Table of n, a(n) for n = 1..300

Example

a(4) = 3: [1,1,1,1], [1,1,2], [1,3];
a(5) = 2: [1,1,1,1,1], [1,2,2];
a(6) = 5: [1,1,1,1,1,1], [1,1,1,1,2], [1,1,1,3], [1,1,4], [1,5];
a(7) = 6: [1,1,1,1,1,1,1], [1,1,1,2,2], [1,1,1,1,3], [1,1,2,3], [1,2,4], [1,1,5];
a(8) = 12: [1,1,1,1,1,1,1,1], [1,1,1,1,1,1,2], [1,1,2,2,2], [1,1,1,2,3], [1,2,2,3], [1,1,3,3], [1,1,1,1,4], [1,3,4], [1,1,1,5], [1,2,5], [3,5], [1,7].

Maple

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

Mathematica

b[n_, j_, t_, s_] := b[n, j, t, s] = Sum[b[n-i, i, t+1, s], {i, j, Quotient[n, 2]}] + If[GCD[t, s] == 1 && GCD[t, n] == 1 && GCD[n, s] == 1, 1, 0]; a[n_] := If[n == 1, 1, Sum [b[n-i, i, 2, i], {i, 1, Quotient[n, 2]}]]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Oct 07 2014, translated from Maple *)

Crossrefs

Cf. A199890.

Sequence in context: A240574 A050061 A058638 * A139140 A047074 A303766

Adjacent sequences: A201215 A201216 A201217 * A201219 A201220 A201221

Keyword

nonn

Author

Alois P. Heinz, Nov 28 2011

Status

approved