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A344353
Numbers that are the sum of four fourth powers in exactly four ways.
7
236674, 282018, 300834, 334818, 478338, 637794, 650034, 650658, 708483, 708834, 729938, 789378, 816578, 832274, 849954, 941859, 989043, 1042083, 1045539, 1099203, 1099458, 1102258, 1179378, 1243074, 1257954, 1283874, 1323234, 1334979, 1339074, 1342979, 1352898, 1357059, 1379043, 1518578
OFFSET
1,1
COMMENTS
Differs from A344352 at term 52 because 2147874 = 2^4 + 14^4 + 31^4 + 33^4 = 4^4 + 23^4 + 27^4 + 34^4 = 7^4 + 21^4 + 28^4 + 34^4 = 12^4 + 17^4 + 29^4 + 34^4 = 14^4 + 18^4 + 19^4 + 37^4.
LINKS
David Consiglio, Jr., Table of n, a(n) for n = 1..20000
EXAMPLE
300834 is a term of this sequence because 300834 = 1^4 + 4^4 + 12^4 + 23^4 = 1^4 + 16^4 + 18^4 + 19^4 = 3^4 + 6^4 + 18^4 + 21^4 = 7^4 + 14^4 + 16^4 + 21^4.
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, 200)]
count = 1
for pos in cwr(power_terms, 4):
tot = sum(pos)
keep[tot] += 1
count += 1
rets = sorted([k for k, v in keep.items() if v == 4])
for x in range(len(rets)):
print(rets[x])
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved