A134618 Numbers such that the sum of cubes of their prime factors (taken with multiplicity) is a prime.

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

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