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A344364
Numbers that are the sum of three fourth powers in five or more ways.
6
292965218, 779888018, 1010431058, 1110995522, 1234349298, 1289202642, 1500533762, 1665914642, 1948502738, 2158376402, 2373191618, 2636686962, 2689817858, 2935465442, 3019732898, 3205282178, 3642994082, 3831800882, 4162186322, 4324686002, 4687443488, 5064808658
OFFSET
1,1
LINKS
EXAMPLE
292965218 is a member of this sequence because 292965218 = 2^4 + 109^4 + 111^4 = 21^4 + 98^4 + 119^4 = 27^4 + 94^4 + 121^4 = 34^4 + 89^4 + 123^4 = 49^4 + 77^4 + 126^4 = 61^4 + 66^4 + 127^4 (actually has 6 representations, so is a member of this sequence but not of A344365).
1234349298 is a member of this sequence because 1234349298 = 7^4 + 154^4 + 161^4 = 26^4 + 143^4 + 169^4 = 61^4 + 118^4 + 179^4 = 74^4 + 107^4 + 181^4 = 91^4 + 91^4 + 182^4.
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, 500)]
for pos in cwr(power_terms, 3):
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
KEYWORD
nonn
AUTHOR
Sean A. Irvine, May 15 2021
STATUS
approved