|
|
A025479
|
|
Largest exponents of perfect powers (A001597).
|
|
15
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
FORMULA
|
|
|
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):
|
|
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.
(PARI) print1(2, ", "); for(k=2, 3^8, if(j=ispower(k), print1(j, ", "))) \\ Hugo Pfoertner, Jan 01 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|