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).
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 25 2022
STATUS
approved