A050703 - OEIS

%I #31 Jul 27 2015 06:08:48

%S 6,10,12,14,15,20,21,26,33,34,35,38,44,46,48,51,55,57,58,65,68,74,85,

%T 86,90,93,96,111,112,116,118,123,135,141,143,145,155,158,161,166,177,

%U 178,185,188,194,201,203,205,206,208,209,210,212,215,221,224,225,252

%N Numbers that when added to the sum of their prime factors (with multiplicity) become prime.

%C No term of this sequence can be prime, since for a prime p, A075254(p)=2*p, hence not prime. - _Michel Marcus_, Jul 24 2015

%C From _Robert Israel_, Jul 24 2015: (Start)

%C Similarly, no term of the sequence can be a prime power.

%C Contains 2*n for n in A023208 and 3*n for n in A023213. (End)

%H K. D. Bajpai, <a href="/A050703/b050703.txt">Table of n, a(n) for n = 1..12180</a>

%F {n: A075254(n) in A000040}. - _R. J. Mathar_, Jul 27 2015

%e 252 = 2*2*3*3*7; 252 + (2 + 2 + 3 + 3 + 7) = 252 + 17 = 269, which is prime.

%p filter:= n ->isprime(convert(map(convert,ifactors(n)[2],`*`),`+`)+n):

%p select(filter, [$1..1000]); # _Robert Israel_, Jul 24 2015

%t upto=300;Rest[Select[Complement[Range[upto], Prime[Range[ PrimePi[upto]]]], PrimeQ[#+ Total[Times@@@FactorInteger[#]]]&]] (* _Harvey P. Dale_, Apr 20 2011 *)

%t Select[Range[500], PrimeQ[# + Total [Times @@@ FactorInteger[#]] && PrimeOmega[#] > 1] &]  (* _K. D. Bajpai_, Sep 12 2014 *)

%o (PARI) sopfr(n)=my(f=factor(n));sum(i=1,#f[,1],f[i,1]*f[i,2])

%o is(n)=!isprime(n)&&isprime(n+sopfr(n)) \\ _Charles R Greathouse IV_, Jul 19 2011

%Y Cf. A050704-A050710, A075254, A023208, A023213.

%K nonn,nice

%O 1,1

%A _Patrick De Geest_, Aug 15 1999

%E Name clarified by _Michel Marcus_, Jul 24 2015