A393485 Areas of Heron triangles whose sides all have prime power lengths.

6, 12, 120, 8160, 33553920

Offset

1,1

Links

Table of n, a(n) for n=1..5.

Florian Luca, Fermat Primes and Heron Triangles with Prime Power Sides, Amer. Math. Monthly, 110 (No. 1, 2003), pp. 46-49.

Formula

For n >= 2, a(n) = 2*(A019434(n) - 2)*(A019434(n-1) - 1).

Example

a(1) is the area of the Heron triangle with side lengths that are all prime powers: 3, 4, and 5.
a(2) is the area of the Heron triangle with side lengths that are all prime powers: 5, 5, and 8.

Prog

(Magma) lst:=[6]; for n in [2..5] do if IsPrime(2^(2^(n-1))+1) then Append(~lst, 2*(2^(2^n/2)-1)*(2^(2^n/4))); end if; end for; lst;

Crossrefs

Cf. A019434, A221837.

Sequence in context: A191662 A095388 A038515 * A335735 A051586 A228858

Adjacent sequences: A393482 A393483 A393484 * A393486 A393487 A393488

Keyword

nonn,hard,more

Author

Arkadiusz Wesolowski, Mar 16 2026

Status

approved