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A340284
Number of partitions of n into 3 parts such that the 'middle' part is relatively prime to each of the other two parts.
2
0, 0, 1, 1, 1, 2, 1, 3, 3, 4, 2, 7, 4, 9, 7, 9, 7, 15, 9, 18, 14, 19, 12, 27, 15, 26, 21, 30, 21, 44, 25, 43, 35, 46, 34, 58, 34, 59, 46, 64, 43, 82, 47, 80, 64, 83, 58, 107, 65, 106, 79, 110, 75, 137, 86, 128, 98, 132, 92, 172, 96, 155, 122, 161, 118, 198, 119, 188, 147
OFFSET
1,6
FORMULA
a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} floor(1/gcd(i,k)) * floor(1/gcd(i,n-i-k)).
MATHEMATICA
Table[Sum[Sum[Floor[1/GCD[i, k]]*Floor[1/GCD[i, n - i - k]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 80}]
CROSSREFS
Sequence in context: A057938 A375729 A144623 * A218975 A048619 A116087
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jan 02 2021
STATUS
approved