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A025478 Least roots of perfect powers (A001597). 18
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; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(n) = A052410(A001597(n)).
(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
EXAMPLE
a(5)=2 because pp(5)=16=2^4 (not 4^2 as we take the smallest base).
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}]]
(* Second program: *)
Prepend[DeleteCases[#, 0], 1] &@ Table[If[Set[e, GCD @@ #[[All, -1]]] > 1, Power[n, 1/e], 0] &@ FactorInteger@ n, {n, 4000}] (* Michael De Vlieger, Apr 25 2017 *)
PROG
(Haskell)
a025478 n = a025478_list !! (n-1) -- a025478_list defined in A001597.
-- Reinhard Zumkeller, Mar 11 2014
CROSSREFS
Cf. A052410 (least root), A001597 (perfect powers).
Cf. A025479 (largest exponents of perfect powers).
Sequence in context: A264662 A076403 A157987 * A084371 A025476 A347731
KEYWORD
easy,nonn
AUTHOR
EXTENSIONS
Added cross-reference. Definition edited by Daniel Forgues, Mar 10 2009
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)