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A305888 Numbers that are the perimeter of a Heronian triangle, but not of a primitive Heronian triangle. 0
24, 88, 280, 472, 558, 664, 696, 852, 856, 1048, 1432, 1720, 1816, 2008, 2180, 2292, 2680, 2776, 2868, 3144, 3352, 3544, 3576, 3582, 3732, 3736, 3860, 3928, 4192, 4308, 4504, 4696, 4878, 4976, 5080, 5172, 5272, 5464, 5598, 5748, 6520, 6616, 6740, 6744, 7188 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers in A051518 that are not in A096468.

LINKS

Table of n, a(n) for n=1..45.

Eric Weisstein's World of Mathematics, Heronian Triangle

EXAMPLE

The only Heronian triangle with perimeter 24 has sides {6, 8, 10} and thus it is not primitive. Hence 24 is in the sequence.

MATHEMATICA

hpp[p_] := Catch@Block[{t=0, c, q=p/2}, Do[c = p-a-b; If[c >= b && a+c > b && a+b > c && IntegerQ@ Sqrt[q (q-a) (q-b) (q-c)], t++; If[GCD[a, b, c] == 1, Throw@ False]], {a, p/3}, {b, a, p-a-1}]; t > 0]; Select[2 Range[350], hpp]

CROSSREFS

Cf. A051518, A096468.

Sequence in context: A044211 A044592 A211632 * A233644 A010012 A256718

Adjacent sequences:  A305885 A305886 A305887 * A305889 A305890 A305891

KEYWORD

nonn

AUTHOR

Giovanni Resta, Jun 14 2018

STATUS

approved

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Last modified September 28 14:44 EDT 2022. Contains 357073 sequences. (Running on oeis4.)