A050705 - OEIS

%I #16 Jul 03 2017 02:05:17

%S 10,12,14,15,20,21,26,33,35,38,44,48,51,65,68,86,93,96,111,112,116,

%T 123,161,188,201,203,206,209,210,215,221,278,297,300,304,306,321,352,

%U 356,371,384,395,398,413,420,441,471,485,524,533,543,545,546,551,570,626

%N Composite number such that when sum of its prime factors is added or subtracted becomes prime.

%C Prime factors counted with multiplicity, e.g., 44 = 2*2*11 so the sum of its prime factors is 15 (not 13). - _Harvey P. Dale_, May 30 2012

%H Harvey P. Dale, <a href="/A050705/b050705.txt">Table of n, a(n) for n = 1..1000</a>

%e E.g., 545 = 5*109 so 545 +- (5+109) = 545 +- 114 = 659 and 431 and both are primes.

%t spfQ[n_]:=Module[{s=Total[Times@@@FactorInteger[n]]},!PrimeQ[n] && PrimeQ[ n+s]&&PrimeQ[n-s]]; Select[Range[700],spfQ] (* _Harvey P. Dale_, May 30 2012 *)

%o (PARI) lista(nn) = {forcomposite(n=2, nn, f = factor(n); sopfr = sum(j=1, #f~, f[j, 1]*f[j, 2]); if (isprime(n+sopfr) && isprime(n-sopfr), print1(n, ", ")););} \\ _Michel Marcus_, Jul 03 2017

%Y Cf. A050703, A050704, A050706, A050707, A050708, A050709, A050710.

%K nonn,nice

%O 1,1

%A _Patrick De Geest_, Aug 15 1999