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A344648
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Numbers that are the sum of three fourth powers in exactly six ways.
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6
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292965218, 1010431058, 1110995522, 1500533762, 1665914642, 2158376402, 2373191618, 2636686962, 2689817858, 3019732898, 3205282178, 3642994082, 3831800882, 4324686002, 4687443488, 5064808658, 5175310322, 6317554418, 6450435362, 6720346178, 7018992162, 7635761042, 7781780258
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OFFSET
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1,1
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COMMENTS
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Differs from A344647 at term 2 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.
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LINKS
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Sean A. Irvine, Table of n, a(n) for n = 1..5000
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EXAMPLE
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1010431058 is a term because 1010431058 = 13^4 + 143^4 + 156^4 = 31^4 + 132^4 + 163^4 = 44^4 + 123^4 + 167^4 = 52^4 + 117^4 + 169^4 = 69^4 + 103^4 + 172^4 = 81^4 + 92^4 + 173^4.
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PROG
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(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 == 6])
for x in range(len(rets)):
print(rets[x])
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CROSSREFS
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Cf. A344365, A344647, A344730, A344921, A345084.
Sequence in context: A204055 A344364 A344647 * A251566 A112452 A291459
Adjacent sequences: A344645 A344646 A344647 * A344649 A344650 A344651
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KEYWORD
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nonn
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AUTHOR
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David Consiglio, Jr., May 25 2021
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STATUS
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approved
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