A343100 Number of partitions of n into 3 parts, at least 2 of which are coprime.
0, 0, 1, 1, 2, 2, 4, 4, 6, 6, 10, 8, 14, 12, 16, 16, 24, 18, 30, 24, 32, 30, 44, 32, 50, 42, 54, 48, 70, 48, 79, 64, 80, 72, 96, 72, 113, 90, 112, 96, 138, 96, 153, 120, 144, 132, 182, 128, 195, 150, 192, 168, 232, 162, 239, 192, 240, 210, 287, 192, 305, 240, 288, 256
Offset: 1
Keywords
Examples
a(12) = 8; [10,1,1], [9,2,1], [8,3,1], [7,4,1], [7,3,2], [6,5,1], [5,5,2], [5,4,3].
Programs
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Mathematica
Table[Sum[Sum[Sign[Floor[1/GCD[i, j]] + Floor[1/GCD[i, n - i - j]] + Floor[1/GCD[j, n - i - j]]], {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 100}]
Formula
a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} sign(floor(1/gcd(i, j)) + floor(1/gcd(i, n-i-j)) + floor(1/gcd(j, n-i-j))).