

A233410


a(n) = smallest multiple m of n such that there are at most m/n perfect powers <= m.


1



1, 2, 3, 20, 45, 60, 77, 96, 117, 180, 209, 276, 312, 378, 420, 464, 510, 594, 646, 700, 756, 814, 874, 936, 1050, 1118, 1188, 1260, 1363, 1440, 1519, 1632, 1716, 1836, 1925, 2016, 2183, 2394, 2496, 2600, 2788, 2898, 3010, 3124, 3330
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OFFSET

1,2


COMMENTS

A perfect power is a power k^e with e != 1 (see A001597).
No value of the sequence belongs to A001597 except the first value 1.


LINKS



EXAMPLE

n=1: a(1)=1 as the only perfect power <= 1 is 1.
n=2: a(2)=2 as the only perfect power <= 2 is 1, and 2=2*1.
n=3: a(3)=3 as the only perfect power <= 3 is 1, and 3=3*1.
n=4: a(4)=20 as (1,4,8,9,16) are 5 perfect powers smaller than 20 and 20 = 4*5.
n=5: a(5)=45 as (1,4,8,9,16,25,27,32,36) are 9 perfect powers smaller than 45 and 45 = 5*9.


PROG

(Python)
def __init__(self) :
def perf_pows_up_to(self, n):
idx = 1
while True:
if self.a001597.at(idx) > n :
return idx1
idx += 1
def at(self, n):
k = 1
while True :
m = k*n
if self.perf_pows_up_to(m) <= k:
return m
k += 1
for n in range(1, 20):


CROSSREFS

Cf. A001597 = list of perfect powers, A069623 = number of perfect powers <= n


KEYWORD

nonn


AUTHOR



STATUS

approved



