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
Keywords
Examples
a(7) = 3 since 7 = 3+4 = 2+5 = 1+6; 7 = 1+2+4 does not count (A036998(7)=4).
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..200
Programs
-
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 *) -
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
Extensions
Terms a(31) and beyond from Andrew Howroyd, Apr 20 2021
Comments