A345563
Numbers that are the sum of six fourth powers in six or more ways.
Original entry on oeis.org
21251, 37811, 38051, 43251, 43571, 43875, 44115, 44531, 45155, 45651, 45891, 47411, 47586, 48276, 49796, 49971, 52195, 53235, 53315, 54131, 56290, 57395, 57460, 57570, 58035, 58500, 59075, 59330, 59780, 59795, 59811, 59860, 60035, 62180, 62211, 63971, 66340
Offset: 1
37811 is a term because 37811 = 1^4 + 2^4 + 2^4 + 7^4 + 11^4 + 12^4 = 2^4 + 2^4 + 4^4 + 7^4 + 9^4 + 13^4 = 2^4 + 3^4 + 6^4 + 6^4 + 9^4 + 13^4 = 3^4 + 4^4 + 8^4 + 8^4 + 11^4 + 11^4 = 4^4 + 6^4 + 7^4 + 9^4 + 9^4 + 12^4 = 5^4 + 5^4 + 9^4 + 10^4 + 10^4 + 10^4.
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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 >= 6])
for x in range(len(rets)):
print(rets[x])
A345609
Numbers that are the sum of seven fifth powers in six or more ways.
Original entry on oeis.org
13562501, 14583968, 21555313, 22057487, 22066065, 23089782, 23345024, 24217918, 24401574, 24855016, 24952718, 24993517, 25052501, 25385064, 28608832, 29558618, 30653536, 31613713, 32559143, 33005785, 33533765, 33635825, 33828631, 34267551, 34268332, 35431351
Offset: 1
14583968 is a term because 14583968 = 1^5 + 4^5 + 14^5 + 16^5 + 19^5 + 21^5 + 23^5 = 2^5 + 4^5 + 14^5 + 14^5 + 20^5 + 22^5 + 22^5 = 4^5 + 5^5 + 10^5 + 15^5 + 20^5 + 21^5 + 23^5 = 6^5 + 8^5 + 9^5 + 15^5 + 15^5 + 20^5 + 25^5 = 6^5 + 8^5 + 14^5 + 14^5 + 14^5 + 16^5 + 26^5 = 6^5 + 10^5 + 12^5 + 12^5 + 16^5 + 16^5 + 26^5.
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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 >= 6])
for x in range(len(rets)):
print(rets[x])
A345719
Numbers that are the sum of six fifth powers in five or more ways.
Original entry on oeis.org
54827300, 74115800, 74883600, 75609125, 113088250, 120274275, 166078869, 169692136, 174781858, 178736448, 182341225, 185558208, 194939538, 203054589, 218814275, 235067008, 250989825, 251772882, 252721458, 255453233, 258124975, 274616694, 282859667
Offset: 1
74115800 is a term because 74115800 = 1^5 + 4^5 + 21^5 + 21^5 + 29^5 + 34^5 = 1^5 + 8^5 + 14^5 + 23^5 + 32^5 + 32^5 = 4^5 + 11^5 + 13^5 + 22^5 + 24^5 + 36^5 = 5^5 + 6^5 + 19^5 + 20^5 + 24^5 + 36^5 = 6^5 + 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, 6):
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])
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])
A345864
Numbers that are the sum of five fifth powers in six or more ways.
Original entry on oeis.org
288203194368, 2784485221024, 6022068333568, 9222502219776, 9670153077344, 10918228000032, 15441787364576
Offset: 1
-
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, 5):
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])
A346361
Numbers that are the sum of six fifth powers in exactly six ways.
Original entry on oeis.org
287718651, 553545456, 746783675, 972232800, 1005620508, 1040741042, 1070652352, 1074892544, 1182426366, 1197332400, 1243267146, 1317183650, 1364866263, 1387455091, 1429663400, 1498160992, 1529189818, 1554833117, 1558594400, 1610298901, 1623782765, 1627228231
Offset: 1
287718651 is a term because 287718651 = 10^5 + 11^5 + 20^5 + 22^5 + 30^5 + 48^5 = 8^5 + 10^5 + 21^5 + 27^5 + 27^5 + 48^5 = 3^5 + 6^5 + 25^5 + 30^5 + 30^5 + 47^5 = 9^5 + 10^5 + 13^5 + 26^5 + 37^5 + 46^5 = 6^5 + 9^5 + 14^5 + 31^5 + 35^5 + 46^5 = 10^5 + 11^5 + 12^5 + 23^5 + 41^5 + 44^5.
-
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 == 6])
for x in range(len(rets)):
print(rets[x])
Showing 1-6 of 6 results.
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