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

1,1

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