OFFSET
1,2
COMMENTS
Vaughan & Wooley (1995) prove that a(n) <= 17 for large enough n; in fact it is conjectured that a(n) <= 6 for large enough n. The maximum value is a(223) = 37. - Charles R Greathouse IV, Jul 05 2017
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
R. C. Vaughan and T. D. Wooley, Waring's problem: a survey, Number theory for the millennium, III (Urbana, IL, 2000), 301-340, A K Peters, Natick, MA, 2002.
Robert C. Vaughan and Trevor D. Wooley, Further improvements in Waring's problem, Acta Mathematica 174:2 (1995), pp. 147-240.
EXAMPLE
33 = 2^5 + 1^5 (least decomposition) hence a(33) = 2.
MATHEMATICA
Cnt5[n_] := Module[{k = 1}, While[Length[PowersRepresentations[n, k, 5]] == 0, k++]; k]; Array[Cnt5, 105] (* T. D. Noe, Apr 01 2011 *)
PROG
(Python)
from itertools import count
from sympy.solvers.diophantine.diophantine import power_representation
def A188462(n):
if n == 1: return 1
for k in count(1):
try:
next(power_representation(n, 5, k))
except:
continue
return k # Chai Wah Wu, Jun 25 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Jean-François Alcover, Apr 01 2011
STATUS
approved