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

1,1

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.

Links

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

Example

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.

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

Crossrefs

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

Sequence in context: A345863 A346257 A345723 * A015398 A034614 A140501

Adjacent sequences: A346361 A346362 A346363 * A346365 A346366 A346367

Keyword

nonn

Author

David Consiglio, Jr., Jul 13 2021

Status

approved