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 A083290 Number of partitions of n into distinct parts which are coprime to n and which are also pairwise relatively prime. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 21 17:21 EDT 2024. Contains 372738 sequences. (Running on oeis4.)