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A025478
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Least roots of perfect powers (A001597).
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14
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1, 2, 2, 3, 2, 5, 3, 2, 6, 7, 2, 3, 10, 11, 5, 2, 12, 13, 14, 6, 15, 3, 2, 17, 18, 7, 19, 20, 21, 22, 2, 23, 24, 5, 26, 3, 28, 29, 30, 31, 10, 2, 33, 34, 35, 6, 11, 37, 38, 39, 40, 41, 12, 42, 43, 44, 45, 2, 46, 3, 13, 47, 48, 7, 50, 51, 52, 14, 53, 54, 55, 5, 56, 57, 58, 15, 59, 60, 61, 62
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Daniel Forgues, Table of n, a(n) for n=1..10000
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FORMULA
| (i) a(n) < n for n>2. (ii) a(n)/n is bounded and lim sup a(n)/n must be around 0.7. (iii) sum(k=1, k, a(k)) seems to be asymptotic to c*n^2 with c around 0.29. (iv) a(n) = 2 if n is in A070228 (proof seems self-evident), hence there's no asymptotic expression for a(n) (just the average in (iii)). - Benoit Cloitre, Oct 14, 2002
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EXAMPLE
| a(5)=2 because pp(5)=16=2^4 (not 4^2 as we take the smallest base).
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MATHEMATICA
| pp = Select[ Range[5000], Apply[GCD, Last[ Transpose[ FactorInteger[ # ]]]] > 1 &]; f[n_] := Block[{b = 2}, While[ !IntegerQ[ Log[b, pp[[n]]]], b++ ]; b]; Join[{1}, Table[ f[n], {n, 2, 80}]]
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CROSSREFS
| a(n) = A052410(A001597(n)).
Cf. A025479 Largest exponents of perfect powers (A001597).
Cf. A001597 Perfect powers: m^k where m is an integer and k >= 2.
Sequence in context: A076397 A076403 A157987 * A084371 A025476 A078773
Adjacent sequences: A025475 A025476 A025477 * A025479 A025480 A025481
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KEYWORD
| easy,nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
| Added cross-reference. Definition edited by Daniel Forgues (squid(AT)zensearch.com), Mar 10 2009
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