|
|
A353742
|
|
Sorted prime metasignature of n.
|
|
13
|
|
|
1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,5
|
|
COMMENTS
|
The prime metasignature counts the multiplicities of each value in the prime signature of n. For example, 2520 has prime indices {1,1,1,2,2,3,4}, sorted prime signature {1,1,2,3}, and sorted prime metasignature {1,1,2}.
|
|
LINKS
|
|
|
EXAMPLE
|
The prime indices, sorted prime signatures, and sorted prime metasignatures of selected n:
n = 1: {} -> {} -> {}
n = 2: {1} -> {1} -> {1}
n = 6: {1,2} -> {1,1} -> {2}
n = 12: {1,1,2} -> {1,2} -> {1,1}
n = 30: {1,2,3} -> {1,1,1} -> {3}
n = 60: {1,1,2,3} -> {1,1,2} -> {1,2}
n = 210: {1,2,3,4} -> {1,1,1,1} -> {4}
n = 360: {1,1,1,2,2,3} -> {1,2,3} -> {1,1,1}
|
|
MATHEMATICA
|
Join@@Table[Sort[Length/@Split[Sort[Last/@If[n==1, {}, FactorInteger[n]]]]], {n, 100}]
|
|
CROSSREFS
|
Positions of first appearances are A182863.
This is the sorted version of A238747.
A001222 counts prime factors with multiplicity.
A003963 gives product of prime indices.
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|