A346257 Numbers that are the sum of five fifth powers in exactly five ways.

9006349824, 65799210368, 67629776576, 181085909632, 188189635424, 295677350451, 467139768468, 471359089024, 656243139157, 691381929281, 797466940832, 854533526901, 874953049024, 891862586132, 953769598750, 1038549256768, 1092458681568, 1182658308657

Offset

1,1

Comments

Differs from 103 terms known at term 6 because 288203194368 = 48^5 + 84^5 + 96^5 + 108^5 + 192^5 = 16^5 + 99^5 + 103^5 + 121^5 + 189^5 = 42^5 + 68^5 + 86^5 + 148^5 + 184^5 = 16^5 + 68^5 + 124^5 + 136^5 + 184^5 = 16^5 + 82^5 + 94^5 + 158^5 + 178^5 = 24^5 + 36^5 + 144^5 + 156^5 + 168^5.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..253

Example

9006349824 is a term because 9006349824 = 24^5 + 42^5 + 48^5 + 54^5 + 96^5 = 21^5 + 34^5 + 43^5 + 74^5 + 92^5 = 8^5 + 34^5 + 62^5 + 68^5 + 92^5 = 8^5 + 41^5 + 47^5 + 79^5 + 89^5 = 12^5 + 18^5 + 72^5 + 78^5 + 84^5.

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, 5):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 5])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A344359, A344519, A345863, A346360.

Sequence in context: A204407 A144651 A345863 * A345723 A346364 A015398

Adjacent sequences: A346254 A346255 A346256 * A346258 A346259 A346260

Keyword

nonn

Author

David Consiglio, Jr., Jul 11 2021

Status

approved