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

Offset: 1

Author

Seiichi Manyama, Jun 25 2024

Keywords

• nonn
• look

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.

Crossrefs

Cf. A002828, A002376, A002377, A188462.

Cf. A002804, A018886.

Programs

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
				

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

Formula

a(n) <= 73.