

A134618


Numbers such that the sum of cubes of their prime factors (taken with multiplicity) is a prime.


9



12, 28, 40, 45, 48, 52, 54, 56, 63, 75, 80, 96, 104, 108, 117, 136, 152, 153, 165, 175, 210, 224, 232, 245, 250, 261, 268, 300, 320, 325, 333, 344, 350, 363, 384, 387, 390, 399, 405, 416, 432, 462, 464, 468, 475, 477, 504, 507, 531, 536, 539, 561, 570, 584
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OFFSET

1,1


LINKS



EXAMPLE

a(2) = 28, since 28 = 2*2*7 and 2^3 + 2^3 + 7^3 = 359 which is prime.


MATHEMATICA

Select[Range[600], PrimeQ[Total[Flatten[Table[#[[1]], {#[[2]]}]&/@ FactorInteger[#]]^3]]&] (* Harvey P. Dale, Feb 01 2013 *)


PROG

(Python)
from sympy import factorint, isprime
def ok(n): return isprime(sum(p**3 for p in factorint(n, multiple=True)))


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



