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 A050703 Numbers that when added to the sum of their prime factors (with multiplicity) become prime. 34
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 21 07:08 EDT 2024. Contains 373540 sequences. (Running on oeis4.)