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 A158804 Composite integers that are a multiple of the sum of their distinct prime factors. 3

%I

%S 4,8,9,16,25,27,30,32,49,60,64,70,81,84,90,105,120,121,125,128,140,

%T 150,168,169,180,231,234,240,243,252,256,260,270,280,286,289,300,315,

%U 336,343,350,360,361,450,456,468,480,490,504,512,520,525,528,529,532,540

%N Composite integers that are a multiple of the sum of their distinct prime factors.

%C Koninck & Luca give upper and lower bounds for the number of elements of this sequence below x: x / exp(c_i(1 + o(1))sqrt(log x log log x)), where the constants c_i and the o(1) differ for lower and upper bounds. - _Charles R Greathouse IV_, Sep 08 2012

%H Charles R Greathouse IV, <a href="/A158804/b158804.txt">Table of n, a(n) for n = 1..10000</a>

%H Jean-Marie de Koninck, Florian Luca, <a href="https://doi.org/10.1112/S0025579300000346">Integers divisible by the sum of their prime factors</a>, Mathematika 52 (1&2) (2005) 69-77, <a href="http://www.ams.org/mathscinet-getitem?mr=2261843">MR2261843</a>.

%F {n in A002808: A008472(n)|n }

%e 4 is in the sequence because A008472(4)=2 divides 4. 5 is not in the sequence because it is prime. 6 is not in the sequence because A008472(6)=5 does not divide 6.

%p A008472 := proc(n) numtheory[factorset](n) ; add(d,d=%) ; end: isbeta := proc(n) if isprime(n) then false; else if n mod A008472(n) = 0 then true; else false; fi; fi; end: for n from 2 to 1200 do if isbeta(n) then printf("%d,",n); fi; od:

%t Select[Range[2,540],!PrimeQ[#]&&IntegerQ[#/Total[First/@FactorInteger[#]]]&] (* _Jayanta Basu_, Jun 02 2013 *)

%o (PARI) is(n)=my(f=factor(n)[,1]);n%sum(i=1,#f,f[i])==0 \\ _Charles R Greathouse IV_, Feb 04 2013

%Y Cf. A002808 (composite numbers), A008472.

%K easy,nonn

%O 1,1

%A _R. J. Mathar_, Mar 27 2009

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Last modified July 24 15:05 EDT 2021. Contains 346273 sequences. (Running on oeis4.)