OFFSET
1,2
COMMENTS
The sequence of runs of a sequence consists of its maximal consecutive constant subsequences when read left-to-right. For example, the runs of (2,2,1,1,1,3,2,2) are (2,2), (1,1,1), (3), (2,2), with sums (4,3,3,4).
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.
This sequence represents the transformation f(P) described by Kimberling at A237685.
LINKS
Mathematics Stack Exchange, What is a sequence run? (answered 2011-12-01)
EXAMPLE
The prime indices of 1260 are {1,1,2,2,3,4}, with run-sums (2,4,3,4), and the multiset {2,3,4,4} has Heinz number 735, so a(1260) = 735.
MATHEMATICA
Table[Times@@Prime/@Cases[If[n==1, {}, FactorInteger[n]], {p_, k_}:>PrimePi[p]*k], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 23 2022
STATUS
approved