

A298676


Number of partitions of n that can be uniquely recovered from their Pgraphs.


0



1, 2, 3, 5, 5, 7, 7, 10, 11, 13, 13, 18, 19, 26, 31, 36, 41, 48, 59, 71, 84, 94, 106, 123, 146, 165, 187, 210, 240, 275, 318, 364, 407, 465, 525, 593, 672, 756, 849, 966, 1080, 1207, 1354, 1530, 1718, 1925, 2135, 2377, 2667, 2997, 3351, 3736, 4141, 4598, 5125
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

a(n) is the number of partitions of n that can be uniquely recovered from its Pgraph, 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

Table of n, a(n) for n=1..55.
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 Pgraph, a single vertex.
a(2) = 2 because both partitions of 2 can be recovered from their corresponding Pgraphs.


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

Sequence in context: A246578 A048947 A222312 * A114519 A126762 A082048
Adjacent sequences: A298673 A298674 A298675 * A298677 A298678 A298679


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



