A201025 Number of partitions of n such that the number of parts and the smallest part are not coprime.

0, 0, 0, 1, 1, 1, 1, 3, 4, 5, 7, 10, 12, 15, 18, 25, 30, 39, 47, 62, 74, 94, 113, 144, 173, 215, 261, 324, 390, 476, 571, 697, 832, 1004, 1196, 1439, 1706, 2038, 2409, 2868, 3380, 4001, 4702, 5550, 6504, 7645, 8938, 10478, 12218, 14277, 16612, 19363, 22481

Offset

1,8

Links

Alois P. Heinz, Table of n, a(n) for n = 1..400

Formula

a(n) = A000041(n) - A200928(n).

Example

a(7) = 1: [2,5];
a(8) = 3: [2,2,2,2], [4,4], [2,6];
a(9) = 4: [2,2,2,3], [3,3,3], [4,5], [2,7];
a(10) = 5: [2,2,3,3], [2,2,2,4], [3,3,4], [4,6], [2,8];
a(11) = 7: [2,3,3,3], [2,2,3,4], [3,4,4], [2,2,2,5], [3,3,5], [4,7], [2,9].

Maple

b:= proc(n, j, t, s) option remember;
      add (b(n-i, i, irem(t+1, s), s), i=j..iquo(n, 2))+
      `if`(igcd(t, s)>1, 1, 0)
    end:
a:= n-> add (b(n-i, i, 2, i), i=2..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, Mod[t+1, s], s], {i, j, Quotient[n, 2]}] + If[GCD[t, s]>1, 1, 0]; a[n_] := Sum [b[n-i, i, 2, i], {i, 2, Quotient[n, 2]}]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Feb 15 2017, translated from Maple *)

Crossrefs

Cf. A000041, A199889, A200928.

Sequence in context: A159560 A288427 A030502 * A288451 A236384 A351741

Adjacent sequences: A201022 A201023 A201024 * A201026 A201027 A201028

Keyword

nonn

Author

Alois P. Heinz, Nov 25 2011

Status

approved