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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 Daniel Forgues, Table of n, a(n) for n=1..10000 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, 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 Adjacent sequences:  A025475 A025476 A025477 * A025479 A025480 A025481 KEYWORD easy,nonn AUTHOR EXTENSIONS Added cross-reference. Definition edited by Daniel Forgues, Mar 10 2009 STATUS approved

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Last modified September 22 02:38 EDT 2021. Contains 347605 sequences. (Running on oeis4.)