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 A004432 Numbers that are the sum of 3 distinct nonzero squares. 27
 14, 21, 26, 29, 30, 35, 38, 41, 42, 45, 46, 49, 50, 53, 54, 56, 59, 61, 62, 65, 66, 69, 70, 74, 75, 77, 78, 81, 83, 84, 86, 89, 90, 91, 93, 94, 98, 101, 104, 105, 106, 107, 109, 110, 113, 114, 115, 116, 117, 118, 120, 121, 122, 125, 126, 129, 131, 133 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers that can be written as a(n) = x^2 + y^2 + z^2 with 0 < x < y < z. This is a subsequence (equal to the range) of A024803. As a set, it is the union of A025339 and A024804, subsequences of numbers having exactly one, resp. more than one, such representations. - M. F. Hasler, Jan 25 2013 Conjecture: a number n is a sum of 3 squares, but not a sum of 3 distinct nonzero squares (i.e., is in A004432 but not A000408), if and only if it is of the form 4^j*s, where j >= 0 and s in {1, 2, 3, 5, 6, 9, 10, 11, 13, 17, 18, 19, 22, 25, 27, 33, 34, 37, 43, 51, 57, 58, 67, 73, 82, 85, 97, 99, 102, 123, 130, 163, 177, 187, 193, 267, 627, 697}. - Jeffrey Shallit, Jan 15 2017 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 FORMULA A004432 = { x^2 + y^2 + z^2; 0 < x < y < z }. n is in A004432 <=> A025442(n) > 0. - M. F. Hasler, Feb 03 2013 EXAMPLE 14 = 1^2 + 2^2 + 3^2; 62 = 1^2 + 5^2 + 6^2. MATHEMATICA f[upto_]:=Module[{max=Floor[Sqrt[upto]]}, Select[Union[Total/@ (Subsets[ Range[ max], {3}]^2)], #<=upto&]]; f  (* Harvey P. Dale, Mar 24 2011 *) PROG (PARI) is_A004432(n)=for(x=1, sqrtint(n\3), for(y=x+1, sqrtint((n-1-x^2)\2), issquare(n-x^2-y^2)&return(1)))  \\ M. F. Hasler, Feb 02 2013 (Haskell) a004432 n = a004432_list !! (n-1) a004432_list = filter (p 3 \$ tail a000290_list) [1..] where    p k (q:qs) m = k == 0 && m == 0 ||                   q <= m && k >= 0 && (p (k - 1) qs (m - q) || p k qs m) -- Reinhard Zumkeller, Apr 22 2013 CROSSREFS Cf. A001974, A024803, A025339, A025442. Cf. A000290, A003995, A004431, A004433, A004434, A224981, A224982, A224983. Sequence in context: A114985 A001944 A024803 * A025339 A224771 A096017 Adjacent sequences:  A004429 A004430 A004431 * A004433 A004434 A004435 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)