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A343708
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Numbers that are the sum of two positive cubes in exactly two ways.
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5
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1729, 4104, 13832, 20683, 32832, 39312, 40033, 46683, 64232, 65728, 110656, 110808, 134379, 149389, 165464, 171288, 195841, 216027, 216125, 262656, 314496, 320264, 327763, 373464, 402597, 439101, 443889, 513000, 513856, 515375, 525824, 558441, 593047, 684019, 704977, 805688, 842751, 885248, 886464
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OFFSET
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1,1
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COMMENTS
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This sequence differs from A001235 at term 455 because 87539319 = 167^3 + 436^3 = 228^3 + 423^3 = 255^3 + 414^3 = A011541(3). Thus, this term is not in this sequence but is in A001235.
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LINKS
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EXAMPLE
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13832 is in this sequence because 13832 = 2^3 + 24^3 = 18^3 + 20^3.
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MATHEMATICA
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Select[Range@70000, Length@Select[PowersRepresentations[#, 2, 3], FreeQ[#, 0]&]==2&] (* Giorgos Kalogeropoulos, Apr 26 2021 *)
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PROG
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(Python)
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)]#n
for pos in cwr(power_terms, 2):#m
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 2])#s
for x in range(len(rets)):
print(rets[x])
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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