A346364 Numbers that are the sum of six fifth powers in exactly nine ways.

9085584992, 16933805856, 37377003050, 39254220544, 41066625600, 41485873792, 42149876800, 43828403850, 44180505600, 45902654525, 48588434400, 52005184992, 53536896864, 54156285568, 56229189632, 57088402525, 59954496800, 63432407850, 66188522400, 66507304800

Offset: 1

Author

David Consiglio, Jr., Jul 13 2021

Keywords

• nonn

Comments

This sequence differs from A345723:

55302546200 = 34^5 + 38^5 + 50^5 + 57^5 + 95^5 + 136^5

= 23^5 + 49^5 + 61^5 + 69^5 + 107^5 + 131^5

= 24^5 + 37^5 + 63^5 + 81^5 + 104^5 + 131^5

= 21^5 + 35^5 + 60^5 + 94^5 + 100^5 + 130^5

= 57^5 + 60^5 + 71^5 + 75^5 + 109^5 + 128^5

= 19^5 + 37^5 + 56^5 + 96^5 + 104^5 + 128^5

= 35^5 + 41^5 + 53^5 + 69^5 + 115^5 + 127^5

= 16^5 + 49^5 + 53^5 + 83^5 + 112^5 + 127^5

= 35^5 + 37^5 + 40^5 + 88^5 + 119^5 + 121^5

= 11^5 + 24^5 + 71^5 + 104^5 + 109^5 + 121^5,

so 55302546200 is in A345723, but is not in this sequence.

Examples

			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 a term.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..549

Crossrefs

Cf. A345723, A345821, A346286, A346363, A346365.

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 == 9])
    for x in range(len(rets)):
        print(rets[x])