|
| |
|
|
A353861
|
|
Number of distinct weak run-sums of the prime indices of n.
|
|
26
|
|
|
|
1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 3, 2, 3, 3, 5, 2, 4, 2, 4, 3, 3, 2, 4, 3, 3, 4, 4, 2, 4, 2, 6, 3, 3, 3, 4, 2, 3, 3, 4, 2, 4, 2, 4, 4, 3, 2, 5, 3, 4, 3, 4, 2, 5, 3, 5, 3, 3, 2, 4, 2, 3, 3, 7, 3, 4, 2, 4, 3, 4, 2, 5, 2, 3, 4, 4, 3, 4, 2, 5, 5, 3, 2, 4, 3, 3, 3
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n ofA112798.
A weak run-sum of a sequence is the sum of any consecutive constant subsequence.
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
The prime indices of 72 are {1,1,1,2,2}, with weak runs {}, {1}, {1,1}, {1,1,1}, {2}, {2,2}, which have sums 0, 1, 2, 3, 2, 4, of which 5 are distinct, so a(72) = 5.
|
|
|
MATHEMATICA
|
Table[Length[Union@@Cases[FactorInteger[n], {p_, k_}:>Range[0, k]*PrimePi[p]]], {n, 100}]
|
|
|
CROSSREFS
|
Positions of first appearances areA000079.
Partitions with distinct run-sums are ranked byA353838,counted byA353837.
The strong version for compositions isA353849.
A005811counts runs in binary expansion.
A353832represents taking run-sums of a partition, compositionsA353847.
A353852ranks compositions with all distinct run-sums, counted byA353850.
Cf.A071625,A073093,A116608,A175413,A181819,A333755,A353834,A353839,A353866,A353867,A353930.
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
