A340754 Number of partitions of n into 4 parts such that the sum of the smallest two parts and the sum of the largest two parts are relatively prime.

0, 0, 0, 0, 0, 1, 0, 3, 1, 4, 2, 11, 1, 18, 7, 14, 11, 39, 10, 54, 14, 40, 31, 94, 26, 99, 53, 101, 49, 185, 34, 225, 102, 162, 123, 220, 96, 378, 174, 269, 160, 511, 117, 588, 229, 354, 314, 764, 235, 747, 318, 607, 395, 1089, 340, 882, 487, 849, 640, 1495, 406, 1650

Offset

0,8

Links

Table of n, a(n) for n=0..61.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} floor(1/gcd(k+j,n-k-j)).

Mathematica

Table[Sum[Sum[Sum[Floor[1/GCD[k + j, n - k - j]], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 80}]

Crossrefs

Sequence in context: A068028 A240058 A275896 * A163359 A065256 A016573

Adjacent sequences: A340751 A340752 A340753 * A340755 A340756 A340757

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 19 2021

Status

approved