A345723 Numbers that are the sum of six fifth powers in nine or more ways.

9085584992, 16933805856, 37377003050, 39254220544, 41066625600, 41485873792, 42149876800, 43828403850, 44180505600, 45902654525, 48588434400, 52005184992, 53536896864, 54156285568, 55302546200, 56229189632, 57088402525, 59954496800, 63432407850

Offset

1,1

Links

Sean A. Irvine, Table of n, a(n) for n = 1..127

Example

16933805856 is a term because 16933805856 = 2^5 + 38^5 + 68^5 + 74^5 + 92^5 + 92^5 = 2^5 + 54^5 + 58^5 + 64^5 + 92^5 + 96^5 = 14^5 + 36^5 + 61^5 + 67^5 + 94^5 + 94^5 = 15^5 + 49^5 + 52^5 + 60^5 + 94^5 + 96^5 = 17^5 + 49^5 + 53^5 + 57^5 + 92^5 + 98^5 = 29^5 + 36^5 + 42^5 + 72^5 + 88^5 + 99^5 = 31^5 + 36^5 + 54^5 + 54^5 + 94^5 + 97^5 = 34^5 + 34^5 + 46^5 + 72^5 + 76^5 + 104^5 = 35^5 + 36^5 + 69^5 + 72^5 + 89^5 + 95^5.

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. A344196, A345566, A345631, A345722, A346364.

Sequence in context: A144651 A345863 A346257 * A346364 A015398 A034614

Adjacent sequences: A345720 A345721 A345722 * A345724 A345725 A345726

Keyword

nonn

Author

David Consiglio, Jr., Jun 24 2021

Status

approved