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 A001974 Numbers that are the sum of 3 distinct squares, i.e., of the form x^2 + y^2 + z^2 with 0 <= x < y < z. 7
 5, 10, 13, 14, 17, 20, 21, 25, 26, 29, 30, 34, 35, 37, 38, 40, 41, 42, 45, 46, 49, 50, 52, 53, 54, 56, 58, 59, 61, 62, 65, 66, 68, 69, 70, 73, 74, 75, 77, 78, 80, 81, 82, 83, 84, 85, 86, 89, 90, 91, 93, 94, 97, 98, 100, 101, 104, 105, 106, 107, 109, 110, 113 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also: Numbers which are the sum of two or three distinct nonzero squares. - M. F. Hasler, Feb 03 2013 According to Halter-Koch (below), a number n is a sum of 3 squares, but not a sum of 3 distinct squares (i.e., is in A001974 but not A000408), if and only if it is of the form 4^j*s, where j >= 0 and s in {1, 2, 3, 6, 9, 11, 18, 19, 22, 27, 33, 43, 51, 57, 67, 99, 102, 123, 163, 177, 187, 267, 627, ?}, where ? denotes at most one unknown number that, if it exists, is > 5*10^10. - Jeffrey Shallit, Jan 15 2017 REFERENCES Franz Halter-Koch, Darstellung natürlicher Zahlen als Summe von Quadraten, Acta Arithmetica 42 (1982), 11-20. LINKS T. D. Noe, Table of n, a(n) for n=1..1000 EXAMPLE 5 = 0^2 + 1^2 + 2^2. MATHEMATICA r[n_] := Reduce[0 <= x < y < z && x^2 + y^2 + z^2 == n, {x, y, z}, Integers]; ok[n_] := r[n] =!= False; Select[ Range[113], ok] (* Jean-François Alcover, Dec 05 2011 *) CROSSREFS Cf. A001983, A024803, A025339, A025442, A004432. Cf. A004436 (complement). Sequence in context: A129846 A194464 A192336 * A242307 A224448 A046130 Adjacent sequences:  A001971 A001972 A001973 * A001975 A001976 A001977 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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