login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A298676 Number of partitions of n that can be uniquely recovered from their P-graphs. 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 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

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 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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 16 21:46 EST 2020. Contains 331975 sequences. (Running on oeis4.)