A083290 Number of partitions of n into distinct parts which are coprime to n and which are also pairwise relatively prime.

1, 0, 1, 1, 2, 1, 3, 2, 3, 2, 7, 2, 9, 3, 4, 5, 16, 3, 20, 4, 8, 7, 31, 5, 22, 9, 18, 9, 54, 4, 68, 16, 21, 16, 28, 11, 112, 20, 32, 18, 144, 9, 173, 22, 33, 40, 221, 19, 139, 25, 71, 43, 327, 25, 117, 47, 103, 80, 475, 18, 568, 90, 98, 122, 191, 29, 805, 93, 197, 44

Offset

1,5

Comments

a(n) <= A036998(n); see A082415 for numbers m with a(m) = A036998(m).

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Example

a(7) = 3 since 7 = 3+4 = 2+5 = 1+6; 7 = 1+2+4 does not count (A036998(7)=4).

Mathematica

a[n_] := a[n] = If[n == 1, 1, Module[{ip}, ip = IntegerPartitions[n, All, Select[Range[n - 1], CoprimeQ[#, n] &]]; Length@Select[ip, Sort[#] == Union[#] && AllTrue[Subsets[#, {2}], CoprimeQ @@ # &] &]]];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 80}] (* Jean-François Alcover, Dec 12 2021 *)

Prog

(PARI) a(n)={local(Cache=Map()); my(recurse(r, p, k)=my(hk=[r, p, k], z); if(!mapisdefined(Cache, hk, &z), z=if(k==0, r==0, self()(r, p, k-1) + if(gcd(p, k)==1, self()(r-k, p*k, min(r-k, k-1)))); mapput(Cache, hk, z)); z); recurse(n, n, n)} \\ Andrew Howroyd, Apr 20 2021

Crossrefs

Cf. A000010, A000586, A007360.

Sequence in context: A323273 A100677 A188637 * A121842 A317963 A219609

Adjacent sequences: A083287 A083288 A083289 * A083291 A083292 A083293

Keyword

nonn

Author

Reinhard Zumkeller, Apr 23 2003

Extensions

Terms a(31) and beyond from Andrew Howroyd, Apr 20 2021

Status

approved