

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
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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((nj)/2)} [gcd(i,j) * gcd(j,nij) * gcd(i,nij) = 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 (Na)/2 do
if igcd(a, b) > 1 then next fi;
ab:= a*b;
for c from b to Nab 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



