This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A307719 Number of partitions of n into 3 mutually coprime parts. 1
 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 LINKS Robert Israel, Table of n, a(n) for n = 0..2000 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. 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}] CROSSREFS Cf. A069905. 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 August 24 03:51 EDT 2019. Contains 326260 sequences. (Running on oeis4.)