A025479 Largest exponents of perfect powers (A001597).

2, 2, 3, 2, 4, 2, 3, 5, 2, 2, 6, 4, 2, 2, 3, 7, 2, 2, 2, 3, 2, 5, 8, 2, 2, 3, 2, 2, 2, 2, 9, 2, 2, 4, 2, 6, 2, 2, 2, 2, 3, 10, 2, 2, 2, 4, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 11, 2, 7, 3, 2, 2, 4, 2, 2, 2, 3, 2, 2, 2, 5, 2, 2, 2, 3, 2, 2, 2, 2, 2, 12, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 8, 2, 3, 2, 2, 2

Offset

1,1

Comments

Greatest common divisor of all prime-exponents in canonical factorization of n-th perfect power. - Reinhard Zumkeller, Oct 13 2002

Asymptotically, 100% of the terms are 2, since the density of cubes and higher powers among the squares and higher powers is 0. - Daniel Forgues, Jul 22 2014

Links

Daniel Forgues, Table of n, a(n) for n=1..10000

Formula

a(n) = A052409(A001597(n)). - Reinhard Zumkeller, Oct 13 2002

A001597(n) = A025478(n)^a(n). - Reinhard Zumkeller, Mar 28 2014

Maple

N:= 10^6: # to get terms corresponding to all perfect powers <= N
V:= Vector(N, storage=sparse);
V[1]:= 2:
for p from 2 to ilog2(N) do
  V[[seq(i^p, i=2..floor(N^(1/p)))]]:= p
od:
r, c, A := ArrayTools:-SearchArray(V):
convert(A, list); # Robert Israel, Apr 25 2017

Mathematica

Prepend[DeleteCases[#, 0], 2] &@ Table[If[Set[e, GCD @@ #[[All, -1]]] > 1, e, 0] &@ FactorInteger@ n, {n, 10^4}] (* Michael De Vlieger, Apr 25 2017 *)

Prog

(Haskell)
a025479 n = a025479_list !! (n-1)  -- a025479_list is defined in A001597.
-- Reinhard Zumkeller, Mar 28 2014, Jul 15 2012
(PARI) print1(2, ", "); for(k=2, 3^8, if(j=ispower(k), print1(j, ", "))) \\ Hugo Pfoertner, Jan 01 2019

Crossrefs

Cf. A001597, A025478, A052409, A124010, A322969.

Sequence in context: A305461 A043261 A157986 * A079243 A093640 A320538

Adjacent sequences: A025476 A025477 A025478 * A025480 A025481 A025482

Keyword

easy,nonn

Author

David W. Wilson

Extensions

Definition corrected by Daniel Forgues, Mar 07 2009

Status

approved