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A212015
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Nonsquare positive integers that are sums of consecutive integer squares.
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4
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2, 5, 6, 10, 13, 14, 15, 19, 28, 29, 30, 31, 35, 41, 44, 50, 54, 55, 56, 60, 61, 69, 77, 85, 86, 90, 91, 92, 96, 105, 110, 113, 126, 135, 139, 140, 141, 145, 146, 149, 154, 170, 174, 181, 182, 190, 194, 195, 199, 203, 204, 205, 209, 218, 221, 230, 231
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OFFSET
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1,1
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COMMENTS
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LINKS
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MAPLE
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filter:= proc(n)
not issqr(n) and
ormap(k -> issqr(-3*k^4+3*k^2+36*k*n) and ((3*k-3*k^2+sqrt(-3*k^4+3*k^2+36*k*n))/(6*k))::integer,
numtheory:-divisors(6*n))
end proc:
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MATHEMATICA
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filterQ[n_] := !IntegerQ[Sqrt[n]] && AnyTrue[Divisors[6n], IntegerQ[Sqrt[-3 #^4 + 3 #^2 + 36 # n]] && IntegerQ[(3 # - 3 #^2 + Sqrt[-3 #^4 + 3 #^2 + 36 # n])/(6#)]&];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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