A346363 Numbers that are the sum of six fifth powers in exactly eight ways.

2295937600, 4335900525, 6251954544, 8986552608, 13413708308, 14539246326, 15277569450, 15728636000, 16770321920, 16873011232, 17572402769, 17713454592, 17960776999, 18190647200, 19621666592, 20570070125, 20827689300, 22322555200, 23461554774, 23613244800

Offset: 1

Author

David Consiglio, Jr., Jul 13 2021

Keywords

• nonn

Comments

This sequence differs from A345722:

9085584992 = 24^5 + 38^5 + 42^5 + 48^5 + 54^5 + 96^5

= 21^5 + 34^5 + 38^5 + 43^5 + 74^5 + 92^5

= 8^5 + 34^5 + 38^5 + 62^5 + 68^5 + 92^5

= 18^5 + 18^5 + 44^5 + 64^5 + 66^5 + 92^5

= 13^5 + 18^5 + 51^5 + 64^5 + 64^5 + 92^5

= 8^5 + 38^5 + 41^5 + 47^5 + 79^5 + 89^5

= 5^5 + 23^5 + 29^5 + 45^5 + 85^5 + 85^5

= 8^5 + 23^5 + 41^5 + 64^5 + 82^5 + 84^5

= 12^5 + 18^5 + 38^5 + 72^5 + 78^5 + 84^5,

so 9085584992 is in A345722, but is not in this sequence.

Examples

			2295937600 =  4^5 + 21^5 + 38^5 + 42^5 + 43^5 + 72^5
           =  8^5 + 16^5 + 30^5 + 42^5 + 54^5 + 70^5
           =  8^5 + 13^5 + 36^5 + 37^5 + 57^5 + 69^5
           = 14^5 + 16^5 + 16^5 + 52^5 + 54^5 + 68^5
           =  3^5 + 14^5 + 32^5 + 44^5 + 61^5 + 66^5
           =  4^5 + 18^5 + 22^5 + 52^5 + 58^5 + 66^5
           = 10^5 + 14^5 + 26^5 + 42^5 + 63^5 + 65^5
           =  1^5 +  7^5 + 34^5 + 57^5 + 58^5 + 63^5,
so 2295937600 is a term.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..4934

Crossrefs

Cf. A345722, A345820, A346285, A346362, A346364.

Programs

Python

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 1000)]
for pos in cwr(power_terms, 6):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 8])
    for x in range(len(rets)):
        print(rets[x])