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

1,1

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)

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A080363 A289558 A082300 * A361126 A330397 A135711

Adjacent sequences: A050700 A050701 A050702 * A050704 A050705 A050706

Keyword

nonn,nice

Author

Patrick De Geest, Aug 15 1999

Extensions

Name clarified by Michel Marcus, Jul 24 2015

Status

approved