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A340280
Number of partitions of n into 3 parts such that the 'middle' part is relatively prime to at least one other part.
2
0, 0, 1, 1, 2, 2, 4, 4, 6, 6, 10, 8, 14, 12, 16, 16, 22, 18, 28, 24, 32, 30, 42, 32, 48, 42, 52, 48, 64, 48, 74, 64, 78, 72, 90, 72, 104, 88, 108, 96, 126, 96, 140, 118, 142, 130, 166, 128, 180, 150, 186, 164, 212, 162, 222, 190, 230, 206, 260, 192, 280, 236, 280, 252
OFFSET
1,5
FORMULA
a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor(1/gcd(i,k)) + floor(1/gcd(i,n-i-k))).
MATHEMATICA
Table[Sum[Sum[Sign[Floor[1/GCD[k, i]] + Floor[1/GCD[i, n - i - k]]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 80}]
CROSSREFS
Sequence in context: A001310 A328422 A029009 * A340279 A343100 A023023
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jan 02 2021
STATUS
approved