A344730 Numbers that are the sum of three fourth powers in exactly seven ways.

779888018, 12478208288, 33038379458, 63170929458, 114872872562, 199651332608, 329296962722, 393006728738, 419200136082, 487430011250, 528614071328, 959702600738, 1010734871328, 1369390032738, 1502549262242, 1525400097858, 1653983981762, 1668273965442, 1756039197458, 1793250582818, 1837965960992, 1912768493202

Offset

1,1

Comments

Differs from A344729 at term 2 because 5745705602 3^4+ 230^4+ 233^4 = 25^4+ 218^4+ 243^4 = 43^4+ 207^4+ 250^4 = 58^4+ 197^4+ 255^4 = 85^4+ 177^4+ 262^4 = 90^4+ 173^4+ 263^4 = 102^4+ 163^4+ 265^4 = 122^4+ 145^4+ 267^4

Links

Sean A. Irvine, Table of n, a(n) for n = 1..86

Example

779888018 is a term because 779888018 = 3^4+ 139^4+ 142^4 = 9^4+ 38^4+ 167^4 = 14^4+ 133^4+ 147^4 = 43^4+ 114^4+ 157^4 = 47^4+ 111^4+ 158^4 = 63^4+ 98^4+ 161^4 = 73^4+ 89^4+ 162^4

Prog

(Python)
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 for x in range(1, 1000)]
for pos in cwr(power_terms, 3):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 7])
for x in range(len(rets)):
    print(rets[x])

Crossrefs

Cf. A344648, A344729, A344738, A344923, A345085.

Sequence in context: A058420 A297867 A344729 * A225389 A166121 A348079

Adjacent sequences: A344727 A344728 A344729 * A344731 A344732 A344733

Keyword

nonn

Author

David Consiglio, Jr., May 27 2021

Status

approved