A340282 Number of partitions of n into 3 parts such that the largest part is relatively prime to at least one other part.

0, 0, 1, 1, 2, 2, 4, 4, 6, 6, 9, 8, 13, 12, 16, 16, 22, 18, 28, 24, 31, 30, 38, 32, 46, 41, 52, 47, 63, 48, 72, 63, 78, 70, 89, 72, 101, 88, 107, 95, 125, 96, 139, 118, 141, 131, 164, 128, 180, 148, 184, 166, 209, 161, 222, 189, 228, 205, 258, 192, 277, 236, 279, 250, 310

Offset

1,5

Links

Table of n, a(n) for n=1..65.

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(n-i-k,k)) + floor(1/gcd(n-i-k,i))).

Mathematica

Table[Sum[Sum[Sign[Floor[1/GCD[n - i - k, k]] + Floor[1/GCD[n - i - k, i]]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 80}]
lppQ[{a_, b_, c_}]:=Total[Boole[{CoprimeQ[c, a], CoprimeQ[b, a]}]]>0; Table[Length[ Select[ IntegerPartitions[n, {3}], lppQ]], {n, 70}] (* Harvey P. Dale, May 08 2022 *)

Crossrefs

Cf. A340279, A340280.

Sequence in context: A238132 A278296 A332305 * A008642 A001364 A029010

Adjacent sequences: A340279 A340280 A340281 * A340283 A340284 A340285

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 02 2021

Status

approved