A340751 - OEIS

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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, 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

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OFFSET

0,8

LINKS

Table of n, a(n) for n=0..64.

Index entries for sequences related to partitions

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

Adjacent sequences: A340748 A340749 A340750 * A340752 A340753 A340754

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jan 19 2021

STATUS

approved