A340280 Number of partitions of n into 3 parts such that the 'middle' part is relatively prime to at least one other part.

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

Links

Table of n, a(n) for n=1..64.

Index entries for sequences related to partitions

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

Cf. A340279, A340282.

Sequence in context: A001310 A328422 A029009 * A340279 A343100 A023023

Adjacent sequences: A340277 A340278 A340279 * A340281 A340282 A340283

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 02 2021

Status

approved