OFFSET
1,6
COMMENTS
A mode in a multiset is an element that appears at least as many times as each of the others. For example, the modes of {a,a,b,b,b,c,d,d,d} are {b,d}.
a(n) depends only on the prime signature of n. - Andrew Howroyd, May 08 2023
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..10000
FORMULA
For n > 1, 1 <= a(n) << log n. - Charles R Greathouse IV, May 09 2023
EXAMPLE
The factorization of 450 is 2*3*3*5*5, modes {3,5}, so a(450) = 2.
The factorization of 900 is 2*2*3*3*5*5, modes {2,3,5}, so a(900) = 3.
The factorization of 1500 is 2*2*3*5*5*5, modes {5}, so a(1500) = 1.
The factorization of 8820 is 2*2*3*3*5*7*7, modes {2,3,7}, so a(8820) = 3.
MATHEMATICA
Table[x=Last/@If[n==1, 0, FactorInteger[n]]; Count[x, Max@@x], {n, 100}]
PROG
(Python)
from sympy import factorint
def A362611(n): return list(v:=factorint(n).values()).count(max(v, default=0)) # Chai Wah Wu, May 08 2023
(PARI) a(n) = if(n==1, 0, my(f=factor(n)[, 2], m=vecmax(f)); #select(v->v==m, f)) \\ Andrew Howroyd, May 08 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 05 2023
STATUS
approved