OFFSET
1,11
LINKS
Tianxin Cai and Deyi Chen, A new variant of the Hilbert-Waring problem, Math. Comp. 82 (2013), 2333-2341.
EXAMPLE
a(11) = 2 because the equation x + y + z = 31 (prime(11)) has exactly 2 solutions with x*y*z = k^3: (x, y, z) = (1, 5, 25) and (1, 12, 18), which satisfy 1*5*25 = 5^3 and 1*12*18 = 6^3.
MATHEMATICA
a[n_] := Length@ Select[ IntegerPartitions[ Prime[n], {3}], IntegerQ[ (Times @@ #)^(1/3)] &]; Array[a, 50] (* Giovanni Resta, Aug 07 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
XU Pingya, Jul 29 2017
STATUS
approved