A289193 Number of ways to represent prime(n)^3 as a sum of 3 distinct primes.
0, 3, 45, 204, 1735, 3640, 13529, 22271, 58302, 182507, 250688, 613046, 1038538, 1311167, 2081983, 3851401, 6675916, 7887193, 12835857, 17422352, 20067757, 30239982, 39351402, 56657043, 88847952, 110134459, 121855019
Offset: 1
Keywords
Examples
a(2)=3: prime(2)=3, and 3^3=27=3+5+19=3+7+17=3+11+13 (3 ways).
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..50
Programs
-
Mathematica
Table[Length@ Select[IntegerPartitions[Prime[n]^3, {3}], And[AllTrue[#, PrimeQ], UnsameQ @@ #] &], {n, 7}] (* Michael De Vlieger, Jun 28 2017 *) -
PARI
a(n)=my(t=prime(n)^3,tp,s); forprime(p=t\3, t-4, tp=t-p; forprime(q=tp\2+1, min(tp, p-1), if(isprime(tp-q), s++))); s \\ Charles R Greathouse IV, Jul 02 2017
Extensions
a(11)-a(27) from Charles R Greathouse IV, Jul 02 2017
Comments