OFFSET
1,1
COMMENTS
If the prime factorization of k has a unique largest exponent, then k is a term.
Numbers whose multiset of prime factors (with multiplicity) has a unique mode. - Gus Wiseman, May 12 2023
Disjoint union of A246655 and A376250. The asymptotic density of this sequence, 0.3660366524547281232052..., is equal to the density of A376250 since the prime powers have a zero density. - Amiram Eldar, Sep 17 2024
LINKS
Jens Ahlström, Table of n, a(n) for n = 1..10000
Wikipedia, Mode (statistics).
EXAMPLE
Prime powers (A246655) are in the sequence, since they have only one prime exponent in their prime factorization, hence a unique largest exponent.
144 is in the sequence, since 144 = 2^4 * 3^2 and there is the unique largest exponent 4.
225 is not in the sequence, since 225 = 3^2 * 5^2 and the largest exponent 2 is not unique, but rather it is the exponent of both the prime factor 3 and of the prime factor 5.
MATHEMATICA
Select[Range[2, 100], Count[(e = FactorInteger[#][[;; , 2]]), Max[e]] == 1 &] (* Amiram Eldar, Sep 01 2022 *)
PROG
(Python)
from sympy import factorint
from collections import Counter
def ok(k):
c = Counter(factorint(k)).most_common(2)
return not (len(c) > 1 and c[0][1] == c[1][1])
print([k for k in range(2, 105) if ok(k)])
(Python)
from sympy import factorint
from itertools import count, islice
def A356862_gen(startvalue=2): # generator of terms >= startvalue
return filter(lambda n:len(f:=sorted(factorint(n).values(), reverse=True))==1 or f[0]!=f[1], count(max(startvalue, 2)))
(PARI) isok(k) = if (k>1, my(f=factor(k), m=vecmax(f[, 2]), w=select(x->(f[x, 2] == m), [1..#f~])); #w == 1); \\ Michel Marcus, Sep 01 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jens Ahlström, Sep 01 2022
STATUS
approved