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 A224771 Numbers that are the sum of 3 distinct and primitive nonzero squares. 3
 14, 21, 26, 29, 30, 35, 38, 41, 42, 45, 46, 49, 50, 53, 54, 59, 61, 62, 65, 66, 69, 70, 74, 75, 77, 78, 81, 83, 86, 89, 90, 91, 93, 94, 98, 101, 105, 106, 107, 109, 110, 113, 114, 115, 117, 118, 121, 122, 125, 126, 129, 131, 133, 134, 137, 138, 139, 141, 142, 145 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence gives the increasingly ordered numbers m which satisfy A224772(m) > 0. This sequence is a proper subsequence of A004432. The first imprimitive members of A004432 are 56, 84, 104, 116, 120, 140, 152, 164, 168, 180, 184, 196, 200, ... LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 FORMULA a(n) is the n-th largest number m which satisfies:  m = a^2 + b^2 + c^2, with integers a, b, and c, 0 < a < b < c, and gcd(a,b,c) = 1. Such a solution is denoted by the triple (a, b, c). EXAMPLE The first triples (a, b, c) are: n=1,  14: (1, 2, 3), n=2,  21: (1, 2, 4), n=3,  26: (1, 3, 4), n=4,  29: (2, 3, 4), n=5,  30: (1, 2, 5), n=6,  35: (1, 3, 5), n=7,  38  (2, 3, 5), n=8,  41: (1, 2, 6), n=9,  42: (1, 4, 5), n=10, 45: (2, 4, 5), ... The first member with two different triples is a(18) = 62 with the triples (1, 5, 6), (2, 3, 7). The first member with three different triples is a(36) = 101  with the triples (1, 6, 8), (2, 4, 9) and (4, 6, 7). MATHEMATICA nn = 150; t = Table[0, {nn^2}]; Do[If[GCD[a, b, c] == 1, n = a^2 + b^2 + c^2; If[n <= nn^2, t[[n]]++]], {a, nn}, {b, a + 1, nn}, {c, b + 1, nn}]; Flatten[Position[t, _?(# > 0 &)]] (* T. D. Noe, Apr 20 2013 *) CROSSREFS Cf. A224772 (multiplicities), A224773 (one half of the even members), A004432, A025442. Sequence in context: A024803 A004432 A025339 * A096017 A274226 A324073 Adjacent sequences:  A224768 A224769 A224770 * A224772 A224773 A224774 KEYWORD nonn AUTHOR Wolfdieter Lang, Apr 19 2013 STATUS approved

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Last modified April 20 03:02 EDT 2021. Contains 343121 sequences. (Running on oeis4.)