cp's OEIS Frontend

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

%I A158804 #17 Jul 22 2020 10:30:34
%S A158804 4,8,9,16,25,27,30,32,49,60,64,70,81,84,90,105,120,121,125,128,140,
%T A158804 150,168,169,180,231,234,240,243,252,256,260,270,280,286,289,300,315,
%U A158804 336,343,350,360,361,450,456,468,480,490,504,512,520,525,528,529,532,540
%N A158804 Composite integers that are a multiple of the sum of their distinct prime factors.
%C A158804 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 A158804 Charles R Greathouse IV, <a href="/A158804/b158804.txt">Table of n, a(n) for n = 1..10000</a>
%H A158804 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 A158804 {n in A002808: A008472(n)|n }
%e A158804 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 A158804 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 A158804 Select[Range[2,540],!PrimeQ[#]&&IntegerQ[#/Total[First/@FactorInteger[#]]]&] (* _Jayanta Basu_, Jun 02 2013 *)
%o A158804 (PARI) is(n)=my(f=factor(n)[,1]);n%sum(i=1,#f,f[i])==0 \\ _Charles R Greathouse IV_, Feb 04 2013
%Y A158804 Cf. A002808 (composite numbers), A008472.
%K A158804 easy,nonn
%O A158804 1,1
%A A158804 _R. J. Mathar_, Mar 27 2009