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%I #10 Jul 01 2018 15:09:29
%S 96,224,360,416,486,504,600,608,792,810,992,1176,1184,1224,1368,1376,
%T 1400,1890,1952,2040,2088,2184,2232,2250,2336,2528,2600,2754,2760,
%U 2904,2952,3080,3104,3296,3384,3480,3510,3640,3726,4064,4158,4248,4312,4392
%N 6-almost primes whose sum of factors is a prime.
%H Charles R Greathouse IV, <a href="/A108609/b108609.txt">Table of n, a(n) for n = 1..10000</a>
%e 96=2*2*2*2*2*3 (6-almost prime) and 2+2+2+2+2+3=13 is a prime.
%t Select[Range[8000], Last[Plus@@FactorInteger[ # ]]==6&&PrimeQ[Plus@@Times@@ Transpose[FactorInteger[ # ]]]&]
%t sfp6Q[n_]:=Module[{pf=Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[n]]}, Length[ pf]==6&&PrimeQ[Total[pf]]]; Select[Range[4400],sfp6Q] (* _Harvey P. Dale_, Jul 01 2018 *)
%o (PARI) is(n)=my(f=factor(n));sum(i=1,#f~,f[i,2])==6 && isprime(sum(i=1,#f~,f[i,1]*f[i,2])) \\ _Charles R Greathouse IV_, Oct 11 2013
%Y Cf. A107707, A108607, A108608 (resp.) 3, 4, 5 (resp.)-almost primes whose sum of factors is a prime.
%K nonn
%O 1,1
%A _Zak Seidov_, Jun 12 2005
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