A050703 Numbers that when added to the sum of their prime factors (with multiplicity) become prime.

6, 10, 12, 14, 15, 20, 21, 26, 33, 34, 35, 38, 44, 46, 48, 51, 55, 57, 58, 65, 68, 74, 85, 86, 90, 93, 96, 111, 112, 116, 118, 123, 135, 141, 143, 145, 155, 158, 161, 166, 177, 178, 185, 188, 194, 201, 203, 205, 206, 208, 209, 210, 212, 215, 221, 224, 225, 252

Offset: 1

Author

Patrick De Geest, Aug 15 1999

Keywords

• nonn
• nice

Comments

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

From Robert Israel, Jul 24 2015: (Start)

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

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

Examples

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

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..12180

Crossrefs

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

Programs

Maple

filter:= n ->isprime(convert(map(convert,ifactors(n)[2],`*`),`+`)+n):
select(filter, [$1..1000]); # Robert Israel, Jul 24 2015

Mathematica

upto=300;Rest[Select[Complement[Range[upto], Prime[Range[ PrimePi[upto]]]], PrimeQ[#+ Total[Times@@@FactorInteger[#]]]&]] (* Harvey P. Dale, Apr 20 2011 *)
Select[Range[500], PrimeQ[# + Total [Times @@@ FactorInteger[#]] && PrimeOmega[#] > 1] &]  (* K. D. Bajpai, Sep 12 2014 *)

PARI

sopfr(n)=my(f=factor(n));sum(i=1,#f[,1],f[i,1]*f[i,2])
is(n)=!isprime(n)&&isprime(n+sopfr(n)) \\ Charles R Greathouse IV, Jul 19 2011

Formula

{n: A075254(n) in A000040}. - R. J. Mathar, Jul 27 2015

Extensions

Name clarified by Michel Marcus, Jul 24 2015