A344359
Numbers that are the sum of five fourth powers in exactly five ways.
Original entry on oeis.org
59779, 67859, 93394, 108274, 112850, 136915, 142354, 151475, 161459, 168979, 181219, 183539, 183604, 185299, 187699, 189394, 193379, 195394, 199090, 199474, 200979, 201874, 202979, 203299, 205859, 211330, 212419, 213730, 217810, 217890, 221779, 223090, 223155, 223714, 226514, 227779, 231235
Offset: 1
93394 is a term of this sequence because 93394 = 1^4 + 4^4 + 8^4 + 14^4 + 15^4 = 1^4 + 6^4 + 12^4 + 12^4 + 15^4 = 1^4 + 9^4 + 10^4 + 14^4 + 14^4 = 5^4 + 6^4 + 11^4 + 14^4 + 14^4 = 5^4 + 7^4 + 8^4 + 12^4 + 16^4.
-
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, 5):
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])
A345863
Numbers that are the sum of five fifth powers in five or more ways.
Original entry on oeis.org
9006349824, 65799210368, 67629776576, 181085909632, 188189635424, 288203194368, 295677350451, 467139768468, 471359089024, 656243139157, 691381929281, 797466940832, 854533526901, 874953049024, 891862586132, 953769598750, 1038549256768
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 >= 5])
for x in range(len(rets)):
print(rets[x])
A342688
Numbers that are the sum of five positive fifth powers in exactly three ways.
Original entry on oeis.org
13124675, 28055699, 50043937, 52679923, 53069024, 55097976, 57936559, 60484744, 62260463, 62445305, 70211956, 73133026, 79401728, 80368962, 84766210, 88512249, 93288865, 98824300, 106993391, 113055482, 117173891, 120968132, 123383875, 126416258, 131106051, 131529588, 132022925
Offset: 1
50043937 = 6^5 + 16^5 + 18^5 + 24^5 + 33^5
= 7^5 + 13^5 + 21^5 + 23^5 + 33^5
= 11^5 + 13^5 + 13^5 + 29^5 + 31^5
so 50043937 is a term of this sequence.
[Corrected by _Patrick De Geest_, Dec 28 2024]
Cf.
A003350,
A004845,
A342685,
A342686,
A342687,
A344244,
A344519,
A344518,
A345863,
A345864,
A346257,
A346358.
-
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, 500)]
for pos in cwr(power_terms, 5):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 3])
for x in range(len(rets)):
print(rets[x])
A344518
Numbers that are the sum of five positive fifth powers in four or more ways.
Original entry on oeis.org
287618651, 1386406515, 1763135232, 2494769760, 2619898293, 3096064443, 3291315732, 3749564512, 4045994624, 5142310350, 5183605813, 5658934676, 5880926107, 7205217018, 7401155424, 7691215599, 8429499101, 8926086432, 9006349824, 9051501568, 9203796832
Offset: 1
287618651 is a term because
287618651 = 8^5 + 21^5 + 27^5 + 27^5 + 48^5
= 9^5 + 13^5 + 26^5 + 37^5 + 46^5
= 11^5 + 12^5 + 23^5 + 41^5 + 44^5
= 11^5 + 20^5 + 22^5 + 30^5 + 48^5.
[Corrected by _Patrick De Geest_, Dec 28 2024]
-
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, 500)]
for pos in cwr(power_terms, 5):
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])
A346360
Numbers that are the sum of six fifth powers in exactly five 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, 287677700
Offset: 1
54827300 is a term because 54827300 = 4^5 + 7^5 + 21^5 + 22^5 + 23^5 + 33^5 = 5^5 + 10^5 + 15^5 + 20^5 + 28^5 + 32^5 = 1^5 + 14^5 + 16^5 + 19^5 + 28^5 + 32^5 = 4^5 + 11^5 + 13^5 + 22^5 + 29^5 + 31^5 = 5^5 + 6^5 + 19^5 + 20^5 + 29^5 + 31^5.
-
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 == 5])
for x in range(len(rets)):
print(rets[x])
A344519
Numbers that are the sum of five positive fifth powers in exactly four ways.
Original entry on oeis.org
287618651, 1386406515, 1763135232, 2494769760, 2619898293, 3096064443, 3291315732, 3749564512, 4045994624, 5142310350, 5183605813, 5658934676, 5880926107, 7205217018, 7401155424, 7691215599, 8429499101, 8926086432, 9051501568, 9203796832, 9254212901
Offset: 1
287618651 is a term because
287618651 = 8^5 + 21^5 + 27^5 + 27^5 + 48^5
= 9^5 + 13^5 + 26^5 + 37^5 + 46^5
= 11^5 + 12^5 + 23^5 + 41^5 + 44^5
= 11^5 + 20^5 + 22^5 + 30^5 + 48^5.
[Corrected by _Patrick De Geest_, Dec 28 2024]
Cf.
A003350,
A004845,
A342685,
A342686,
A342687,
A342688,
A344244,
A344355,
A344518,
A345863,
A345864,
A346257,
A346358,
A346359.
-
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, 500)]
for pos in cwr(power_terms, 5):
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])
Showing 1-6 of 6 results.
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