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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Harvey P. Dale and Hieronymus Fischer, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)
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)))
print([k for k in range(585) if ok(k)]) # Michael S. Branicky, Dec 28 2021
CROSSREFS
Sequence in context: A087252 A141274 A224613 * A108405 A184838 A044073
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, Nov 11 2007
EXTENSIONS
Example clarified by Harvey P. Dale, Feb 01 2013
Minor edits by Hieronymus Fischer, May 06 2013
STATUS
approved

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Last modified June 16 23:34 EDT 2024. Contains 373432 sequences. (Running on oeis4.)