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A289193 Number of ways to represent prime(n)^3 as a sum of 3 distinct primes. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

From the ternary Goldbach conjecture.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..50

FORMULA

a(n) = A125688(A030078(n)).

EXAMPLE

a(2)=3: prime(2)=3, and 3^3=27=3+5+19=3+7+17=3+11+13 (3 ways).

MATHEMATICA

Table[Length@ Select[IntegerPartitions[Prime[n]^3, {3}], And[AllTrue[#, PrimeQ], UnsameQ @@ #] &], {n, 7}] (* Michael De Vlieger, Jun 28 2017 *)

PROG

(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

CROSSREFS

Cf. A030078, A068307, A007963, A125688.

Sequence in context: A093585 A062270 A069955 * A062346 A002682 A073595

Adjacent sequences:  A289190 A289191 A289192 * A289194 A289195 A289196

KEYWORD

nonn

AUTHOR

Zak Seidov, Jun 28 2017

EXTENSIONS

a(11)-a(27) from Charles R Greathouse IV, Jul 02 2017

STATUS

approved

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Last modified October 18 10:28 EDT 2017. Contains 293507 sequences.