A344927
Numbers that are the sum of four fourth powers in exactly nine ways.
Original entry on oeis.org
328118259, 385202034, 395613234, 489597858, 625839858, 641398338, 674511618, 693239634, 699598578, 722302434, 779889314, 780278643, 782999714, 791204514, 792005379, 797405714, 797935698, 805299699, 815120658, 822938754, 851527314, 857962914, 870861618
Offset: 1
328118259 is a term because 328118259 = 2^4 + 77^4 + 109^4 + 111^4 = 8^4 + 79^4 + 93^4 + 121^4 = 18^4 + 79^4 + 97^4 + 119^4 = 21^4 + 77^4 + 98^4 + 119^4 = 27^4 + 77^4 + 94^4 + 121^4 = 34^4 + 77^4 + 89^4 + 123^4 = 46^4 + 57^4 + 103^4 + 119^4 = 49^4 + 77^4 + 77^4 + 126^4 = 61^4 + 66^4 + 77^4 + 127^4.
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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, 4):
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])
A344738
Numbers that are the sum of three fourth powers in exactly eight ways.
Original entry on oeis.org
5745705602, 8185089458, 11054952818, 14355295682, 21789116258, 22247419922, 26839201298, 29428835618, 31861462178, 37314202562, 38214512882, 41923075922, 46543615202, 51711350418, 54438780578, 56255300738, 59223741122, 62862779042, 63429959138, 71035097042
Offset: 1
5745705602 is a term because 5745705602 = 3^4 + 230^4 + 233^4 = 25^4 + 218^4 + 243^4 = 43^4 + 207^4 + 250^4 = 58^4 + 197^4 + 255^4 = 85^4 + 177^4 + 262^4 = 90^4 + 173^4 + 263^4 = 102^4 + 163^4 + 265^4 = 122^4 + 145^4 + 267^4.
-
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, 1000)]
for pos in cwr(power_terms, 3):
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])
A344750
Numbers that are the sum of three fourth powers in nine or more ways.
Original entry on oeis.org
49511121842, 105760443698, 131801075042, 187758243218, 253590205778, 281539574498, 319889609522, 364765611938, 401069383442, 445600096578, 510334859762, 541692688082, 601395185762, 615665999858, 703409488418, 730871934338, 749472385298, 792177949472
Offset: 1
105760443698 is a term because 105760443698 = 7^4 + 476^4 + 483^4 = 51^4 + 452^4 + 503^4 = 76^4 + 437^4 + 513^4 = 107^4 + 417^4 + 524^4 = 133^4 + 399^4 + 532^4 = 199^4 + 348^4 + 547^4 = 212^4 + 337^4 + 549^4 = 228^4 + 323^4 + 551^4 = 252^4 + 301^4 + 553^4.
-
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, 1000)]
for pos in cwr(power_terms, 3):
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])
A345120
Numbers that are the sum of three third powers in exactly nine ways.
Original entry on oeis.org
14926248, 16819704, 20168784, 44946000, 45580536, 54042624, 59768064, 62099136, 66203136, 67956624, 69393024, 78008832, 78716448, 79539832, 80621568, 80996544, 89354448, 90757584, 99616392, 100088568, 101352168, 101943360, 112216896, 112720896, 114306984
Offset: 1
14926248 is a term because 14926248 = 2^3 + 33^3 + 245^3 = 11^3 + 185^3 + 203^3 = 14^3 + 32^3 + 245^3 = 50^3 + 113^3 + 236^3 = 71^3 + 89^3 + 239^3 = 74^3 + 189^3 + 196^3 = 89^3 + 185^3 + 197^3 = 98^3 + 148^3 + 219^3 = 105^3 + 149^3 + 217^3.
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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, 1000)]
for pos in cwr(power_terms, 3):
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])
A344861
Numbers that are the sum of three fourth powers in exactly ten ways.
Original entry on oeis.org
49511121842, 364765611938, 703409488418, 792177949472, 2667500248322, 3602781562562, 3999861055442, 4010400869202, 5698033074818, 5836249791008, 6330685395762, 7250378688098, 7695882509378, 8746828790882, 10383571090802, 11254551814688, 12160605587858
Offset: 1
49511121842 is a term because 49511121842 = 13^4 + 390^4 + 403^4 = 35^4 + 378^4 + 413^4 = 70^4 + 357^4 + 427^4 = 103^4 + 335^4 + 438^4 = 117^4 + 325^4 + 442^4 = 137^4 + 310^4 + 447^4 = 175^4 + 322^4 + 441^4 = 182^4 + 273^4 + 455^4 = 202^4 + 255^4 + 457^4 = 225^4 + 233^4 + 458^4.
-
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, 1000)]
for pos in cwr(power_terms, 3):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 10])
for x in range(len(rets)):
print(rets[x])
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