|
| |
|
|
A362613
|
|
Number of co-modes in the prime factorization of n.
|
|
44
|
|
|
|
0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 3, 1, 1, 2, 3, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 2, 1, 2, 2, 2, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,6
|
|
|
COMMENTS
|
First differs from A327500 at n = 180.
First differs from A351946 at n = 180.
First differs from A353507 at n = 180.
We define a co-mode in a multiset to be an element that appears at most as many times as each of the others. For example, the co-modes of {a,a,b,b,b,c,c} are {a,c}.
a(n) depends only on the prime signature of n. - Andrew Howroyd, May 08 2023
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
The factorization of 180 is 2*2*3*3*5, co-modes {5}, so a(180) = 1.
The factorization of 900 is 2*2*3*3*5*5, co-modes {2,3,5}, so a(900) = 3.
The factorization of 8820 is 2*2*3*3*5*7*7, co-modes {5}, so a(8820) = 1.
|
|
|
MATHEMATICA
|
Table[x=Last/@If[n==1, 0, FactorInteger[n]]; Count[x, Min@@x], {n, 100}]
|
|
|
PROG
|
(Python)
from sympy import factorint
v = factorint(n).values()
w = min(v, default=0)
return sum(1 for e in v if e<=w) # Chai Wah Wu, May 08 2023
(PARI) a(n) = if(n==1, 0, my(f=factor(n)[, 2], m=vecmin(f)); #select(v->v==m, f)) \\ Andrew Howroyd, May 08 2023
|
|
|
CROSSREFS
|
Positions of first appearances are A002110.
Counting partitions by this statistic (co-mode count) gives A362615.
A027746 lists prime factors (with multiplicity).
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
