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A340751
Number of partitions of n into 4 parts such that both the smallest two parts and the largest two parts are relatively prime.
0
0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 9, 11, 15, 13, 20, 21, 26, 28, 34, 32, 46, 44, 56, 54, 70, 62, 87, 80, 100, 94, 126, 105, 152, 127, 167, 154, 197, 171, 232, 200, 256, 237, 292, 251, 349, 291, 378, 336, 419, 355, 497, 405, 528, 458, 583, 487, 680, 549, 700, 620, 786
OFFSET
0,8
FORMULA
a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} floor(1/gcd(k,j)) * Sum_{i=j..floor((n-j-k)/2)} floor(1/gcd(i,n-i-j-k)).
MATHEMATICA
Table[Sum[Sum[Sum[Floor[1/GCD[k, j]]*Floor[1/GCD[i, n - i - j - k]], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 80}]
CROSSREFS
Sequence in context: A261772 A153156 A017852 * A319069 A029013 A114096
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jan 19 2021
STATUS
approved