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Numbers that are divisible by the sum of their distinct prime factors (A008472).
11

%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