A224771 Numbers that are the sum of 3 distinct and primitive nonzero squares.

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

Offset: 1

Author

Wolfdieter Lang, Apr 19 2013

Keywords

• nonn

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, ...

Examples

			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).
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A224772 (multiplicities), A224773 (one half of the even members), A004432, A025442.

Programs

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 *)

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).