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A070088 Number of prime integer triangles with perimeter n. 11
0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 2, 1, 2, 0, 1, 0, 1, 0, 1, 1, 2, 0, 3, 1, 3, 0, 2, 0, 2, 0, 3, 1, 3, 0, 5, 1, 5, 0, 4, 0, 3, 0, 5, 1, 5, 0, 4, 0, 4, 0, 2, 0, 3, 0, 5, 1, 3, 0, 6, 1, 8, 0, 5, 0, 5, 0, 4, 0, 3, 0, 5, 1, 6, 0, 6, 0, 4, 0, 7, 1, 7, 0, 9, 1, 10, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,15

COMMENTS

a(n) = A070090(n) + A070092(n) = A070095(n) + A070103(n).

LINKS

Table of n, a(n) for n=1..90.

R. Zumkeller, Integer-sided triangles

EXAMPLE

For n=15 there are A005044(15)=7 integer triangles: [1,7,7], [2,6,7], [3,5,7], [3,6,6], [4,4,7], [4,5,6] and [5,5,5]: two of them consist of primes, therefore a(15)=2.

MATHEMATICA

triangleQ[sides_] := With[{s = Total[sides]/2}, AllTrue[sides, # < s&]];

a[n_] := Select[IntegerPartitions[n, {3}, Select[Range[Ceiling[n/2]], PrimeQ]], triangleQ] // Length; Array[a, 90] (* Jean-Fran├žois Alcover, Jul 09 2017 *)

CROSSREFS

Cf. A070080, A070081, A070082, A070097, A070100, A070105, A070108, A070111.

Sequence in context: A143374 A277899 A283760 * A131851 A104886 A215604

Adjacent sequences:  A070085 A070086 A070087 * A070089 A070090 A070091

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 05 2002

STATUS

approved

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Last modified February 17 17:27 EST 2018. Contains 299296 sequences. (Running on oeis4.)