%I #24 Jul 15 2020 04:33:29
%S 2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,29,30,31,32,37,41,43,47,49,53,
%T 59,60,61,64,67,70,71,73,79,81,83,84,89,90,97,101,103,105,107,109,113,
%U 120,121,125,127,128,131,137,139,140,149,150,151,157,163,167,168,169,173
%N Numbers that are divisible by the sum of their distinct prime factors (A008472).
%C The Koninck & Luca bound of x / exp(c(1 + o(1))sqrt(log x log log x)) on A158804 applies equally to this sequence. - _Charles R Greathouse IV_, Sep 08 2012
%H Charles R Greathouse IV, <a href="/A089352/b089352.txt">Table of n, a(n) for n = 1..10000</a>
%H Jean-Marie de Koninck, Florian Luca, <a href="http://dx.doi.org/10.1112/S0025579300000346">Integers divisible by the sum of their prime factors</a>, Mathematika 52:1-2 (2005), pp. 69-77.
%e 84=2*2*3*7 is divisible by 2+3+7.
%t primeDivisors[n_] := Select[Divisors[n], PrimeQ]; primeSumDivQ[n_] := 0 == Mod[n, Apply[Plus, primeDivisors[n]]]; Select[Range[2, 300], primeSumDivQ]
%t Select[Range[2, 175], Divisible[#, Plus @@ First /@ FactorInteger[#]] &] (* _Jayanta Basu_, Aug 13 2013 *)
%o (PARI) is(n)=my(f=factor(n)[,1]);n%sum(i=1,#f,f[i])==0 \\ _Charles R Greathouse IV_, Feb 01 2013
%Y Cf. A008472 (sopf).
%Y Different from A071139.
%K easy,nonn
%O 1,1
%A Ramin Naimi (rnaimi(AT)oxy.edu), Dec 26 2003
%E Name edited by _Michel Marcus_, Jul 15 2020