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A064825
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Numbers which are the sums of three positive triangular numbers in exactly two different ways.
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6
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12, 17, 19, 21, 22, 23, 26, 27, 28, 31, 32, 33, 34, 35, 39, 41, 42, 43, 44, 46, 47, 51, 54, 56, 62, 64, 65, 68, 74, 80, 88, 89, 90, 92, 95, 106, 113, 123, 128, 137, 141, 146, 153, 164, 179, 194, 200, 218, 245, 281, 326, 335
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OFFSET
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1,1
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COMMENTS
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Checked up to 1000000 but haven't found any other values.
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LINKS
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EXAMPLE
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19 = 10 + 6 + 3 = 15 + 3 + 1.
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PROG
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(Magma) [k:k in [1..350]|#RestrictedPartitions(k, 3, {m*(m+1) div 2:m in [1..200]}) eq 2 ]; // Marius A. Burtea, Jan 01 2020
(Python)
from collections import Counter
from itertools import count, takewhile, combinations_with_replacement as mc
def aupto(N):
tris = takewhile(lambda x: x <= N, (i*(i+1)//2 for i in count(1)))
sum3 = filter(lambda x: x <= N, (sum(c) for c in mc(tris, 3)))
sum3counts = Counter(sum3)
return sorted(k for k in sum3counts if sum3counts[k] == 2)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 23 2001
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EXTENSIONS
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STATUS
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approved
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