cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A050703 #31 Jul 27 2015 06:08:48
%S A050703 6,10,12,14,15,20,21,26,33,34,35,38,44,46,48,51,55,57,58,65,68,74,85,
%T A050703 86,90,93,96,111,112,116,118,123,135,141,143,145,155,158,161,166,177,
%U A050703 178,185,188,194,201,203,205,206,208,209,210,212,215,221,224,225,252
%N A050703 Numbers that when added to the sum of their prime factors (with multiplicity) become prime.
%C A050703 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 A050703 From _Robert Israel_, Jul 24 2015: (Start)
%C A050703 Similarly, no term of the sequence can be a prime power.
%C A050703 Contains 2*n for n in A023208 and 3*n for n in A023213. (End)
%H A050703 K. D. Bajpai, <a href="/A050703/b050703.txt">Table of n, a(n) for n = 1..12180</a>
%F A050703 {n: A075254(n) in A000040}. - _R. J. Mathar_, Jul 27 2015
%e A050703 252 = 2*2*3*3*7; 252 + (2 + 2 + 3 + 3 + 7) = 252 + 17 = 269, which is prime.
%p A050703 filter:= n ->isprime(convert(map(convert,ifactors(n)[2],`*`),`+`)+n):
%p A050703 select(filter, [$1..1000]); # _Robert Israel_, Jul 24 2015
%t A050703 upto=300;Rest[Select[Complement[Range[upto], Prime[Range[ PrimePi[upto]]]], PrimeQ[#+ Total[Times@@@FactorInteger[#]]]&]] (* _Harvey P. Dale_, Apr 20 2011 *)
%t A050703 Select[Range[500], PrimeQ[# + Total [Times @@@ FactorInteger[#]] && PrimeOmega[#] > 1] &]  (* _K. D. Bajpai_, Sep 12 2014 *)
%o A050703 (PARI) sopfr(n)=my(f=factor(n));sum(i=1,#f[,1],f[i,1]*f[i,2])
%o A050703 is(n)=!isprime(n)&&isprime(n+sopfr(n)) \\ _Charles R Greathouse IV_, Jul 19 2011
%Y A050703 Cf. A050704-A050710, A075254, A023208, A023213.
%K A050703 nonn,nice
%O A050703 1,1
%A A050703 _Patrick De Geest_, Aug 15 1999
%E A050703 Name clarified by _Michel Marcus_, Jul 24 2015