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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 Cf. A001597, A025475, A134333, A134344, A134376. Cf. A134600, A134602, A134605, A134608, A134612, A134616, A134620. Sequence in context: A087252 A141274 A224613 * A108405 A184838 A044073 Adjacent sequences: A134615 A134616 A134617 * A134619 A134620 A134621 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.)