|
|
A353832
|
|
Heinz number of the multiset of run-sums of the prime indices of n.
|
|
57
|
|
|
1, 2, 3, 3, 5, 6, 7, 5, 7, 10, 11, 9, 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, 25, 41, 42, 43, 33, 35, 46, 47, 21, 19, 26, 51, 39, 53, 26, 55, 35, 57, 58, 59, 45, 61, 62, 49, 13, 65, 66, 67, 51
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
FORMULA
|
|
|
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
|
The number of distinct prime factors of a(n) is A353835, weak A353861.
A353838 ranks partitions with all distinct run-sums, counted by A353837.
Cf. A005811, A047966, A071625, A073093, A181819, A182850, A182857, A304660, A323014, A353834, A353839.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|