A343967
Numbers that are the sum of three positive cubes in five or more ways.
Original entry on oeis.org
161568, 262683, 314712, 326808, 359568, 443197, 444536, 471960, 503208, 513729, 515376, 526023, 529199, 532683, 552824, 597960, 702729, 736371, 746992, 806688, 844416, 863379, 907479, 924048, 931419, 975213, 1011067, 1028663, 1062937, 1092853, 1152152, 1172016, 1211048, 1232496, 1258011
Offset: 1
314712 = 4^3 + 6^3 + 68^3
= 5^3 + 24^3 + 67^3
= 6^3 + 30^3 + 66^3
= 31^3 + 41^3 + 60^3
= 36^3 + 48^3 + 54^3
so 314712 is a term of this sequence.
-
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1,50)]
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])
A344356
Numbers that are the sum of four fourth powers in five or more ways.
Original entry on oeis.org
2147874, 2266338, 2690658, 3189603, 3464178, 3754674, 3847554, 4030419, 4165794, 4457298, 4884114, 5229378, 5624739, 5978883, 5980178, 5981283, 6014178, 6044418, 6134994, 6258723, 6313953, 6400194, 6576339, 6593538, 6612354, 6899603, 7088898, 7498323, 7811874, 7918498, 8064018, 8292323
Offset: 1
2690658 is a term of this sequence because 2690658 = 2^4 + 8^4 + 33^4 + 35^4 = 3^4 + 4^4 + 19^4 + 40^4 = 7^4 + 8^4 + 30^4 + 37^4 = 9^4 + 21^4 + 30^4 + 36^4 = 16^4 + 25^4 + 32^4 + 33^4.
-
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, 50)]
for pos in cwr(power_terms, 4):
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])
A344277
Numbers that are the sum of three fourth powers in four or more ways.
Original entry on oeis.org
5978882, 15916082, 20621042, 22673378, 30623138, 33998258, 39765362, 48432482, 53809938, 61627202, 65413922, 74346818, 84942578, 88258898, 95662112, 103363442, 117259298, 128929682, 131641538, 137149922, 143244738, 155831858, 158811842, 167042642, 174135122, 175706258, 188529362
Offset: 1
20621042 is a member of this sequence because 20621042 = 5^4 + 54^4 + 59^4 = 10^4 + 51^4 + 61^4 = 25^4 + 46^4 + 63^4 = 26^4 + 39^4 + 65^4
-
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 for x in range(1,50)]
for pos in cwr(power_terms,3):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v >= 4])
for x in range(len(rets)):
print(rets[x])
A344365
Numbers that are the sum of three fourth powers in exactly five ways.
Original entry on oeis.org
1234349298, 1289202642, 1948502738, 2935465442, 4162186322, 5632212978, 7360969778, 8657437698, 8753497298, 11079947522, 15784025138, 17536524642, 19749588768, 20627242272, 21318234098, 31176043808, 35240346162, 37459676898, 39912730578, 42901649042
Offset: 1
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.
-
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])
A344647
Numbers that are the sum of three fourth powers in six or more ways.
Original entry on oeis.org
292965218, 779888018, 1010431058, 1110995522, 1500533762, 1665914642, 2158376402, 2373191618, 2636686962, 2689817858, 3019732898, 3205282178, 3642994082, 3831800882, 4324686002, 4687443488, 5064808658, 5175310322, 5745705602, 6317554418, 6450435362, 6720346178, 7018992162
Offset: 1
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
-
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])
Showing 1-5 of 5 results.