The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A307719 Number of partitions of n into 3 mutually coprime parts. 31
 0, 0, 0, 1, 1, 1, 2, 1, 3, 2, 4, 2, 7, 2, 8, 4, 8, 4, 15, 4, 16, 7, 15, 7, 26, 7, 23, 11, 26, 10, 43, 9, 35, 16, 38, 16, 54, 14, 49, 23, 54, 18, 79, 18, 66, 31, 64, 25, 100, 25, 89, 36, 85, 31, 127, 35, 104, 46, 104, 39, 167, 36, 125, 58, 129, 52, 185, 45 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS The Heinz numbers of these partitions are the intersection of A014612 (triples) and A302696 (pairwise coprime). - Gus Wiseman, Oct 16 2020 LINKS Fausto A. C. Cariboni, Table of n, a(n) for n = 0..10000 (terms 0..2000 from Robert Israel) FORMULA a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} [gcd(i,j) * gcd(j,n-i-j) * gcd(i,n-i-j) = 1], where [] is the Iverson bracket. a(n > 2) = A220377(n) + 1. - Gus Wiseman, Oct 15 2020 EXAMPLE There are 2 partitions of 9 into 3 mutually coprime parts: 7+1+1 = 5+3+1, so a(9) = 2. There are 4 partitions of 10 into 3 mutually coprime parts: 8+1+1 = 7+2+1 = 5+4+1 = 5+3+2, so a(10) = 4. There are 2 partitions of 11 into 3 mutually coprime parts: 9+1+1 = 7+3+1, so a(11) = 2. There are 7 partitions of 12 into 3 mutually coprime parts: 10+1+1 = 9+2+1 = 8+3+1 = 7+4+1 = 6+5+1 = 7+3+2 = 5+4+3, so a(12) = 7. MAPLE N:= 200: # to get a(0)..a(N) A:= Array(0..N): for a from 1 to N/3 do   for b from a to (N-a)/2 do     if igcd(a, b) > 1 then next fi;     ab:= a*b;     for c from b to N-a-b do        if igcd(ab, c)=1 then A[a+b+c]:= A[a+b+c]+1 fi od od od: convert(A, list); # Robert Israel, May 09 2019 MATHEMATICA Table[Sum[Sum[Floor[1/(GCD[i, j] GCD[j, n - i - j] GCD[i, n - i - j])], {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 0, 100}] Table[Length[Select[IntegerPartitions[n, {3}], CoprimeQ@@#&]], {n, 0, 100}] (* Gus Wiseman, Oct 15 2020 *) CROSSREFS A023022 is the version for pairs. A220377 is the strict case, with ordered version A220377*6. A327516 counts these partitions of any length, with strict version A305713 and Heinz numbers A302696. A337461 is the ordered version. A337563 is the case with no 1's. A337599 is the pairwise non-coprime instead of pairwise coprime version. A337601 only requires the distinct parts to be pairwise coprime. A001399(n-3) = A069905(n) = A211540(n+2) counts 3-part partitions. A002865 counts partitions with no 1's, with strict case A025147. A007359 and A337485 count pairwise coprime partitions with no 1's. A200976 and A328673 count pairwise non-coprime partitions. Cf. A007304, A014612, A078374, A082024, A284825, A304709, A337462, A337605. Sequence in context: A179080 A294199 A078658 * A185314 A285120 A282744 Adjacent sequences:  A307716 A307717 A307718 * A307720 A307721 A307722 KEYWORD nonn,look AUTHOR Wesley Ivan Hurt, Apr 24 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 20 03:02 EDT 2021. Contains 343121 sequences. (Running on oeis4.)