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A052410
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Write n = m^k with m, k integers, k >= 1, then a(n) is the smallest possible choice for m.
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88
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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
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OFFSET
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1,2
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COMMENTS
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Value of m in m^p = n, where p is the largest possible power (see A052409).
For n > 1, n is a perfect power iff a(n) <> n. - Reinhard Zumkeller, Oct 13 2002
a(n)^A052409(n) = n. - Reinhard Zumkeller, Apr 06 2014
Every integer root of n is a power of a(n). All entries (except 1) belong to A007916. - Gus Wiseman, Sep 11 2017
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LINKS
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Daniel Forgues, Table of n, a(n) for n=1..100000
Eric Weisstein's World of Mathematics, Power
Eric Weisstein's World of Mathematics, Perfect Power
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FORMULA
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a(A001597(k)) = A025478(k).
a(n) = A007916(A278028(n,1)). - Gus Wiseman, Sep 11 2017
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MATHEMATICA
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Table[If[n==1, 1, n^(1/(GCD@@(Last/@FactorInteger[n])))], {n, 100}]
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PROG
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(Haskell)
a052410 n = product $ zipWith (^)
(a027748_row n) (map (`div` (foldl1 gcd es)) es)
where es = a124010_row n
-- Reinhard Zumkeller, Jul 15 2012
(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
# M. Eren Kesim, Jun 03 2021
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CROSSREFS
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Cf. A001597, A025478, A007916, A027748, A052409, A072775, A124010, A175781, A278028, A288636, A289023.
Sequence in context: A019555 A243074 A304776 * A327501 A175781 A072775
Adjacent sequences: A052407 A052408 A052409 * A052411 A052412 A052413
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KEYWORD
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nonn
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AUTHOR
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Eric W. Weisstein
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EXTENSIONS
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Definition edited (in a complementary form to A052409) by Daniel Forgues, Mar 14 2009
Corrected by Charles R Greathouse IV, Sep 02 2009
Definition edited by N. J. A. Sloane, Sep 03 2010
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STATUS
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approved
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