login
Composite numbers k such that sum of prime factors of k + number of prime factors of k = prime.
0

%I #5 Aug 01 2015 10:35:47

%S 6,14,18,24,26,30,38,56,66,70,72,74,86,90,96,98,104,120,126,130,134,

%T 138,150,152,154,158,162,174,190,194,198,206,218,224,238,248,254,266,

%U 280,286,288,294,296,306,310,318,326,338,342,344,350,354,360,370,378,386

%N Composite numbers k such that sum of prime factors of k + number of prime factors of k = prime.

%e 6(2+3+2=7), 14(2+7+2=11), 18(2+3+3+3=11), 24(2+2+2+3+4=13), 26(2+13+2=17), 30(2+3+5+3=13), 38(2+19+2=23), 56(2+2+2+7+4=17)

%t fQ[n_] := Block[ {fi = Flatten[ Table[ First@#, {Last@#}] & /@ FactorInteger@n]}, !PrimeQ@n && PrimeQ[ Plus @@ fi + Length@ fi]]; Rest@ Select[ Range@ 400, fQ@# &] (* _Robert G. Wilson v_, Mar 14 2009 *)

%Y Cf. A000040, A002808.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Mar 12 2009, May 10 2009

%E a(39)-a(56) from _Robert G. Wilson v_, Mar 14 2009