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

Author

Hieronymus Fischer, Nov 11 2007

Keywords

• nonn

Examples

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

Links

• Harvey P. Dale and Hieronymus Fischer, Table of n, a(n) for n = 1..10000 (first 1000 terms from _Harvey P. Dale_)

Crossrefs

Cf. A001597, A025475, A134333, A134344, A134376.

Cf. A134600, A134602, A134605, A134608, A134612, A134616, A134620.

Programs

Mathematica

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

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

Formula

{k: A224787(k) in A000040}. - R. J. Mathar, Mar 25 2025

Extensions

Example clarified by Harvey P. Dale, Feb 01 2013

Minor edits by Hieronymus Fischer, May 06 2013