|
|
A353842
|
|
Last part of the trajectory of the partition run-sum transformation of n, using Heinz numbers.
|
|
6
|
|
|
1, 2, 3, 3, 5, 6, 7, 5, 7, 10, 11, 7, 13, 14, 15, 7, 17, 14, 19, 15, 21, 22, 23, 15, 13, 26, 13, 21, 29, 30, 31, 11, 33, 34, 35, 21, 37, 38, 39, 13, 41, 42, 43, 33, 35, 46, 47, 21, 19, 26, 51, 39, 53, 26, 55, 35, 57, 58, 59, 35, 61, 62, 19, 13, 65, 66, 67, 51
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This gives a bijective correspondence between positive integers and integer partitions.
The run-sum trajectory is obtained by repeatedly taking the run-sum transformation (A353832) until a squarefree number is reached. For example, the trajectory 12 -> 9 -> 7 corresponds to the partitions (2,1,1) -> (2,2) -> (4).
|
|
LINKS
|
|
|
EXAMPLE
|
The partition run-sum trajectory of 87780 is: 87780 -> 65835 -> 51205 -> 19855 -> 2915, so a(87780) = 2915.
|
|
MATHEMATICA
|
Table[NestWhile[Times@@Prime/@Cases[If[#==1, {}, FactorInteger[#]], {p_, k_}:>PrimePi[p]*k]&, n, !SquareFreeQ[#]&], {n, 100}]
|
|
CROSSREFS
|
The fixed points and image are A005117.
Other sequences pertaining to partition trajectory are A353841-A353846.
A353832 represents the operation of taking run-sums of a partition.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|