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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

Index entries for sequences related to partitions

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

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Last modified August 24 03:51 EDT 2019. Contains 326260 sequences. (Running on oeis4.)