A345565
Numbers that are the sum of six fourth powers in eight or more ways.
Original entry on oeis.org
58035, 59780, 87746, 88595, 96195, 96450, 102371, 106451, 106515, 108035, 108275, 108290, 108771, 112370, 112931, 115251, 122835, 122850, 122915, 124691, 125971, 132546, 133395, 133571, 133586, 134675, 134931, 136931, 138275, 138595, 143650, 144755, 144835
Offset: 1
59780 is a term because 59780 = 1^4 + 1^4 + 1^4 + 5^4 + 12^4 + 14^4 = 1^4 + 1^4 + 6^4 + 6^4 + 9^4 + 15^4 = 1^4 + 2^4 + 9^4 + 10^4 + 11^4 + 13^4 = 1^4 + 4^4 + 7^4 + 7^4 + 8^4 + 15^4 = 1^4 + 7^4 + 7^4 + 9^4 + 10^4 + 14^4 = 2^4 + 5^4 + 6^4 + 11^4 + 11^4 + 13^4 = 3^4 + 7^4 + 8^4 + 10^4 + 11^4 + 13^4 = 5^4 + 6^4 + 7^4 + 7^4 + 11^4 + 14^4.
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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, 6):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 8])
for x in range(len(rets)):
print(rets[x])
A345630
Numbers that are the sum of seven fifth powers in eight or more ways.
Original entry on oeis.org
36620574, 80552143, 81401376, 82078424, 92347417, 93653176, 94486699, 94626949, 98873875, 105674625, 110276376, 121050874, 124732805, 125959393, 127808693, 129228307, 130298618, 134581976, 144209018, 145340799, 147245218, 147898763, 151727082
Offset: 1
80552143 is a term because 80552143 = 1^5 + 4^5 + 21^5 + 21^5 + 23^5 + 29^5 + 34^5 = 1^5 + 8^5 + 14^5 + 23^5 + 23^5 + 32^5 + 32^5 = 1^5 + 8^5 + 16^5 + 19^5 + 27^5 + 28^5 + 34^5 = 3^5 + 12^5 + 13^5 + 14^5 + 28^5 + 31^5 + 32^5 = 3^5 + 14^5 + 17^5 + 18^5 + 18^5 + 27^5 + 36^5 = 4^5 + 11^5 + 13^5 + 22^5 + 23^5 + 24^5 + 36^5 = 5^5 + 6^5 + 19^5 + 20^5 + 23^5 + 24^5 + 36^5 = 6^5 + 23^5 + 25^5 + 25^5 + 25^5 + 29^5 + 30^5.
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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, 7):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 8])
for x in range(len(rets)):
print(rets[x])
A345721
Numbers that are the sum of six fifth powers in seven or more ways.
Original entry on oeis.org
1184966816, 1700336000, 1717860100, 1972000800, 2229475325, 2295937600, 2396275200, 2548597632, 2625460992, 2886251808, 3217068800, 3697267200, 3729261536, 3765398725, 4046532448, 4165116967, 4246566632, 4286704224, 4335900525, 4489548050
Offset: 1
1700336000 is a term because 1700336000 = 4^5 + 17^5 + 31^5 + 37^5 + 43^5 + 68^5 = 6^5 + 9^5 + 10^5 + 23^5 + 60^5 + 62^5 = 6^5 + 14^5 + 16^5 + 50^5 + 50^5 + 64^5 = 7^5 + 25^5 + 30^5 + 54^5 + 56^5 + 58^5 = 8^5 + 21^5 + 23^5 + 27^5 + 57^5 + 64^5 = 9^5 + 21^5 + 22^5 + 29^5 + 53^5 + 66^5 = 13^5 + 32^5 + 35^5 + 38^5 + 45^5 + 67^5.
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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, 6):
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])
A345723
Numbers that are the sum of six fifth powers in nine or more ways.
Original entry on oeis.org
9085584992, 16933805856, 37377003050, 39254220544, 41066625600, 41485873792, 42149876800, 43828403850, 44180505600, 45902654525, 48588434400, 52005184992, 53536896864, 54156285568, 55302546200, 56229189632, 57088402525, 59954496800, 63432407850
Offset: 1
16933805856 = 2^5 + 38^5 + 68^5 + 74^5 + 92^5 + 92^5
= 2^5 + 54^5 + 58^5 + 64^5 + 92^5 + 96^5
= 14^5 + 36^5 + 61^5 + 67^5 + 94^5 + 94^5
= 15^5 + 49^5 + 52^5 + 60^5 + 94^5 + 96^5
= 17^5 + 49^5 + 53^5 + 57^5 + 92^5 + 98^5
= 29^5 + 36^5 + 42^5 + 72^5 + 88^5 + 99^5
= 31^5 + 36^5 + 54^5 + 54^5 + 94^5 + 97^5
= 34^5 + 34^5 + 46^5 + 72^5 + 76^5 + 104^5
= 35^5 + 36^5 + 69^5 + 72^5 + 89^5 + 95^5
so 16933805856 is a term.
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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, 6):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 9])
for x in range(len(rets)):
print(rets[x])
A346363
Numbers that are the sum of six fifth powers in exactly eight ways.
Original entry on oeis.org
2295937600, 4335900525, 6251954544, 8986552608, 13413708308, 14539246326, 15277569450, 15728636000, 16770321920, 16873011232, 17572402769, 17713454592, 17960776999, 18190647200, 19621666592, 20570070125, 20827689300, 22322555200, 23461554774, 23613244800
Offset: 1
2295937600 = 4^5 + 21^5 + 38^5 + 42^5 + 43^5 + 72^5
= 8^5 + 16^5 + 30^5 + 42^5 + 54^5 + 70^5
= 8^5 + 13^5 + 36^5 + 37^5 + 57^5 + 69^5
= 14^5 + 16^5 + 16^5 + 52^5 + 54^5 + 68^5
= 3^5 + 14^5 + 32^5 + 44^5 + 61^5 + 66^5
= 4^5 + 18^5 + 22^5 + 52^5 + 58^5 + 66^5
= 10^5 + 14^5 + 26^5 + 42^5 + 63^5 + 65^5
= 1^5 + 7^5 + 34^5 + 57^5 + 58^5 + 63^5,
so 2295937600 is a term.
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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, 6):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 8])
for x in range(len(rets)):
print(rets[x])
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