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A290399 Number of solutions to Diophantine equation x + y + z = prime(n) with xyz = k^3 (0 < x <= y <= z). 0
0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 1, 2, 3, 2, 1, 3, 2, 2, 2, 3, 1, 2, 3, 3, 3, 4, 3, 5, 2, 1, 5, 1, 4, 3, 3, 3, 3, 4, 5, 3, 3, 6, 3, 2, 3, 5, 5, 3, 6, 8, 2, 3, 7, 5, 7, 3, 5, 7, 5, 4, 1, 7, 4, 1, 8, 6, 5, 4, 5, 4, 7, 4, 9, 6, 6, 5, 8, 5, 7, 6, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,11

LINKS

Table of n, a(n) for n=1..86.

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 xyz = 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

Cf. A000040, A000578, A233386.

Sequence in context: A272760 A054717 A086421 * A109400 A202389 A210868

Adjacent sequences:  A290396 A290397 A290398 * A290400 A290401 A290402

KEYWORD

nonn

AUTHOR

XU Pingya, Jul 29 2017

STATUS

approved

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Last modified October 17 07:05 EDT 2018. Contains 316276 sequences. (Running on oeis4.)