A374012 - OEIS

A374012

Least number of 6th powers needed to represent n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

a(703) = 73.

REFERENCES

Pillai, S. S. (1940) On Waring’s problem g(6) = 73. Proc. Indian Acad. Sci. 12A: 30-40

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Waring's Problem.

FORMULA

a(n) <= 73.

PROG

(PARI) a_vector(n, k=6) = my(v=vector(n), cnt=0, d=0, p=1, s=sum(j=1, sqrtnint(n, k), x^j^k)+x*O(x^n)); while(cnt<n, d++; p*=s; for(i=1, n, if(!v[i] && polcoef(p, i), v[i]=d; cnt++))); v;

(Python)

from itertools import count

from sympy.solvers.diophantine.diophantine import power_representation

def A374012(n):

if n == 1: return 1

for k in count(1):

try:

next(power_representation(n, 6, k))

except:

continue

return k # Chai Wah Wu, Jun 25 2024

CROSSREFS