

A215579


Integral averages of three distinct squares.


1



7, 10, 14, 15, 18, 22, 23, 25, 26, 27, 28, 30, 31, 35, 38, 39, 40, 42, 43, 46, 47, 49, 50, 51, 54, 55, 56, 57, 58, 60, 62, 63, 65, 66, 67, 70, 71, 72, 73, 74, 75, 78, 79, 81, 82, 83, 86, 87, 88, 90, 91, 92, 94, 95, 97, 98, 99, 100, 102, 103, 104, 105, 106
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

7 = (1^2 + 2^2 + 4^2)/3
10 = (1^2 + 2^2 + 5^2)/3
14 = (1^2 + 4^2 + 5^2)/3
First case with 2 ways: 23 = (1^2 + 2^2 + 8^2)/3 = (2^2 + 4^2 + 7^2)/3
42 has 3 sets of triples {a,b,c} such that 42= (a^2 + b^2 + c^2)/3: {1,2,11}, {1,5,10}, {3,6,9}
63 has 4 sets of triples {a,b,c}: {2,4,13}, {2,8,11}, {3,6,12}, {5,8,10}, etc.


LINKS



MATHEMATICA

Take[Select[Mean/@Subsets[Range[20]^2, {3}], IntegerQ]//Union, 70] (* Harvey P. Dale, Aug 16 2016 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



