OFFSET
1,2
COMMENTS
a(n) is the number of partitions of n that can be uniquely recovered from its P-graph, the simple graph whose vertices are the parts of the partition, two of which are joined by an edge if, and only if, they have a common factor greater than 1.
LINKS
Bernardo Recamán Santos, A unique partition of 200 into 6 parts, Puzzling Stack Exchange, Dec 17 2017.
EXAMPLE
a(1) = 1 because the sole partition of 1 can be recovered from its P-graph, a single vertex.
a(2) = 2 because both partitions of 2 can be recovered from their corresponding P-graphs.
MATHEMATICA
pgraph[p_] := With[{v = Range[Length[p]]}, Graph[v, UndirectedEdge @@@ Select[Subsets[v, {2}], !CoprimeQ @@ p[[#]] &]]];
a[n_] := Count[Length /@ Gather[pgraph /@ IntegerPartitions[n], IsomorphicGraphQ], 1];
Array[a, 20]
(* Andrey Zabolotskiy, Jan 30 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernardo Recamán, Jan 28 2018
EXTENSIONS
a(23)-a(50) from Freddy Barrera, Jan 29 2018
a(51)-a(55) from Andrey Zabolotskiy, Jan 30 2018
STATUS
approved