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

1,1

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.

Links

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

Example

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.

Prog

(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])

Crossrefs

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

Sequence in context: A180688 A225760 A345722 * A022240 A251490 A277720

Adjacent sequences: A346360 A346361 A346362 * A346364 A346365 A346366

Keyword

nonn

Author

David Consiglio, Jr., Jul 13 2021

Status

approved