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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
Sequence in context: A178508 A123834 A064629 * A306469 A059752 A080205
KEYWORD
nonn
AUTHOR
Zak Seidov, Aug 16 2012
STATUS
approved

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Last modified May 21 15:47 EDT 2024. Contains 372738 sequences. (Running on oeis4.)