The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A308069 Number of integer-sided triangles with perimeter n whose side lengths are semiprime. 1

%I #11 Sep 17 2020 16:21:59

%S 0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,1,1,0,1,2,1,2,1,1,1,1,2,2,1,2,3,4,

%T 2,1,1,2,2,1,0,1,1,2,4,4,2,2,2,3,4,4,5,5,4,7,6,4,2,3,5,4,2,2,3,3,3,5,

%U 8,6,6,7,7,8,7,7,10,9,9,10,12,14,10,7,9

%N Number of integer-sided triangles with perimeter n whose side lengths are semiprime.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>

%F a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * c(i) * c(k) * c(n-i-k), where c is the semiprime characteristic (A064911).

%t Table[Sum[Sum[KroneckerDelta[PrimeOmega[i], 2] KroneckerDelta[PrimeOmega[k], 2] KroneckerDelta[PrimeOmega[n - i - k], 2]*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]

%Y Cf. A064911.

%K nonn

%O 1,22

%A _Wesley Ivan Hurt_, May 10 2019

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 17 18:39 EDT 2024. Contains 375990 sequences. (Running on oeis4.)