%I #28 Aug 02 2022 17:27:35

%S 16,27,30,60,70,105,220,231,286,476,627,646,805,897,1160,1276,1581,

%T 1776,1798,2322,2408,2967,3055,3196,3526,4028,4543,5360,5487,6248,

%U 6461,6745,7198,7881,7968,9628,9717,10366,10707,10864,11036,14231,15368,15836,16377,19304

%N Numbers which, when divided by the sum of their prime factors, give a prime number.

%C One of the prime factors of n disappears in the sum of its prime factors’ prime factors. The sequence includes 2p(p+2) whenever p and p+2 are twin primes. There are no primes or semiprimes in the sequence.

%H Charles R Greathouse IV, <a href="/A199013/b199013.txt">Table of n, a(n) for n = 1..1000</a>

%e 220/(2+2+5+11)=220/20=11, which is prime, so 220 is in the sequence.

%t dspfQ[n_]:=Module[{c=Total[Flatten[Table[#[[1]],{#[[2]]}]&/@FactorInteger[ n]]]}, PrimeQ[n/c]]; Select[Range[20000],dspfQ] (* _Harvey P. Dale_, Mar 19 2013 *)

%o (PARI) is(n)=my(f=factor(n),t);for(i=1,#f[,1],t+=f[i,1]*f[i,2]);if(t&&n%t,0,isprime(n/t)) \\ _Charles R Greathouse IV_, Nov 06 2011

%Y Subsequence of A046346.

%K nonn

%O 1,1

%A _Nico Brown_, Nov 06 2011

%E a(22) corrected, a(30)-a(46) from _Charles R Greathouse IV_, Nov 06 2011