A200476 Number of partitions of n such that the number of parts and the largest part and the smallest part are pairwise not coprime.

0, 0, 0, 1, 0, 1, 0, 3, 1, 3, 1, 8, 3, 9, 6, 16, 9, 24, 17, 35, 29, 49, 45, 81, 73, 110, 115, 166, 166, 240, 250, 347, 372, 491, 539, 715, 776, 988, 1109, 1393, 1553, 1935, 2178, 2676, 3034, 3674, 4176, 5056, 5734, 6862, 7834, 9316, 10615, 12576, 14341, 16890

Offset

1,8

Comments

See comments in A199891, which apply to this sequence also.

Links

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

Example

a(8)  = 3: [2,6], [4,4], [2,2,2,2];
a(9)  = 1: [3,3,3];
a(10) = 3: [2,8], [4,6], [2,2,2,4];
a(11) = 1: [2,2,3,4];
a(12) = 8: [2,10], [4,8], [6,6], [3,3,6], [2,2,2,6], [2,2,4,4], [2,3,3,4], [2,2,2,2,2,2].

Maple

b:= proc(n, j, t, k) option remember;
      add(b(n-i, i, t+1, k), i=j..iquo(n, 2))+
      `if`(igcd(n, t)>1 and igcd(k, t)>1 and igcd(n, k)>1, 1, 0)
    end:
a:= n-> add(b(n-j, j, 2, j), j=2..iquo(n, 2)):
seq(a(n), n=1..70);

Mathematica

b[n_, j_, t_, k_] := b[n, j, t, k] = Sum[b[n-i, i, t+1, k], {i, j, Quotient[n, 2]}] + If[GCD[n, t]>1 && GCD[k, t]>1 && GCD[n, k]>1, 1, 0]; a[n_] := Sum [b[n-j, j, 2, j], {j, 2, Quotient[n, 2]}]; Table[a[n], {n, 1, 70}] (* Jean-François Alcover, Feb 06 2017, translated from Maple *)

Crossrefs

Cf. A199891.

Sequence in context: A349619 A082495 A329385 * A300251 A016572 A072860

Adjacent sequences: A200473 A200474 A200475 * A200477 A200478 A200479

Keyword

nonn

Author

Alois P. Heinz, Nov 18 2011

Status

approved