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A025478 Least roots of perfect powers (A001597). 16
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[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 A078773

Adjacent sequences:  A025475 A025476 A025477 * A025479 A025480 A025481

KEYWORD

easy,nonn

AUTHOR

David W. Wilson

EXTENSIONS

Added cross-reference. Definition edited by Daniel Forgues, Mar 10 2009

STATUS

approved

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Last modified November 17 10:59 EST 2019. Contains 329225 sequences. (Running on oeis4.)