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A371148
Let n = Product_{j=1..k} p_j^e_j and gpf(n)! = Product_{j=1..k} p_j^f_j, where p_j = A000040(j) is the j-th prime and p_k = gpf(n) = A006530(n) is the greatest prime factor of n. a(n) is the numerator of the maximum of e_j/f_j.
5
1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 3, 2, 1, 3, 1, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 4, 2, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 4, 4, 1, 1, 1, 1, 1, 1, 1
OFFSET
2,3
LINKS
Pontus von Brömssen, Table of n, a(n) for n = 2..10000
FORMULA
A362333(n) = ceiling(a(n)/A371149(n)).
EXAMPLE
For n = 80 = 2^4 * 3^0 * 5^1, gpf(80)! = 5! = 2^3 * 3^1 * 5^1. The ratios of the prime exponents are 4/3, 0/1, and 1/1, the greatest of which is 4/3, so a(80) = 4.
PROG
(Python)
from sympy import factorint, Rational
def A371148(n):
f = factorint(n)
gpf = max(f, default=None)
a = 0
for p in f:
m = gpf
v = 0
while m >= p:
m //= p
v += m
a = max(a, Rational(f[p], v))
return a.p
CROSSREFS
Cf. A000040, A006530, A362333, A371149 (denominators), A371150, A371151.
Sequence in context: A302035 A307907 A362333 * A088388 A070013 A070014
KEYWORD
nonn,frac
AUTHOR
STATUS
approved