A340283 Number of partitions of n into 3 parts such that the smallest part is relatively prime to each of the other two parts.

0, 0, 1, 1, 2, 2, 3, 4, 4, 5, 6, 8, 7, 10, 9, 12, 11, 17, 13, 20, 16, 21, 18, 29, 21, 31, 26, 35, 27, 46, 29, 46, 37, 50, 39, 62, 40, 63, 51, 70, 50, 87, 54, 85, 69, 88, 65, 112, 71, 111, 84, 112, 81, 140, 89, 134, 103, 138, 99, 178, 105, 164, 131, 171, 126, 207, 125, 195, 152

Offset

1,5

Links

Robert Israel, Table of n, a(n) for n = 1..2000

Index entries for sequences related to partitions

Formula

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

Maple

f:= proc(n) local k, t;
  t:= 0:
  for k from 1 to floor(n/3) do
    t:= t + nops(select(s -> igcd(s, k) = 1 and igcd(n-s, k) = 1, [$k..(n-k)/2]))
  od;
  t
end proc:
map(f, [$1..100]); # Robert Israel, Nov 25 2024

Mathematica

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

Crossrefs

Cf. A340284, A340285.

Sequence in context: A029043 A296371 A337601 * A324744 A097920 A029042

Adjacent sequences: A340280 A340281 A340282 * A340284 A340285 A340286

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 02 2021

Status

approved