|
|
A052410
|
|
Write n = m^k with m, k integers, k >= 1, then a(n) is the smallest possible choice for m.
|
|
99
|
|
|
1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 12, 13, 14, 15, 2, 17, 18, 19, 20, 21, 22, 23, 24, 5, 26, 3, 28, 29, 30, 31, 2, 33, 34, 35, 6, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 7, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 2, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Value of m in m^p = n, where p is the largest possible power (see A052409).
Every integer root of n is a power of a(n). All entries (except 1) belong to A007916. - Gus Wiseman, Sep 11 2017
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Power
|
|
FORMULA
|
|
|
MATHEMATICA
|
Table[If[n==1, 1, n^(1/(GCD@@(Last/@FactorInteger[n])))], {n, 100}]
|
|
PROG
|
(Haskell)
a052410 n = product $ zipWith (^)
(a027748_row n) (map (`div` (foldl1 gcd es)) es)
where es = a124010_row n
(PARI) a(n) = if (ispower(n, , &r), r, n); \\ Michel Marcus, Jul 19 2017
(Python)
def upto(n):
list = [1] + [0] * (n - 1)
for i in range(2, n + 1):
if not list[i - 1]:
j = i
while j <= n:
list[j - 1] = i
j *= i
return list
(Python)
from math import gcd
from sympy import integer_nthroot, factorint
def A052410(n): return integer_nthroot(n, gcd(*factorint(n).values()))[0] if n>1 else 1 # Chai Wah Wu, Mar 02 2024
|
|
CROSSREFS
|
Cf. A001597, A025478, A007916, A027748, A052409, A072775, A124010, A175781, A278028, A288636, A289023.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|