A134618 - OEIS

%I #17 Dec 28 2021 10:30:07

%S 12,28,40,45,48,52,54,56,63,75,80,96,104,108,117,136,152,153,165,175,

%T 210,224,232,245,250,261,268,300,320,325,333,344,350,363,384,387,390,

%U 399,405,416,432,462,464,468,475,477,504,507,531,536,539,561,570,584

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

%H Harvey P. Dale and Hieronymus Fischer, <a href="/A134618/b134618.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from _Harvey P. Dale_)

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

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

%o (Python)

%o from sympy import factorint, isprime

%o def ok(n): return isprime(sum(p**3 for p in factorint(n, multiple=True)))

%o print([k for k in range(585) if ok(k)]) # _Michael S. Branicky_, Dec 28 2021

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

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

%K nonn

%O 1,1

%A _Hieronymus Fischer_, Nov 11 2007

%E Example clarified by _Harvey P. Dale_, Feb 01 2013

%E Minor edits by _Hieronymus Fischer_, May 06 2013