cp's OEIS Frontend

A066031 Composite numbers n the sum of whose prime factors divides n, but which are not themselves powers of primes.

%I A066031 #18 Feb 03 2016 09:16:39
%S A066031 30,60,70,84,90,105,120,140,150,168,180,231,234,240,252,260,270,280,
%T A066031 286,300,315,336,350,360,450,456,468,480,490,504,520,525,528,532,540,
%U A066031 560,572,588,600,627,646,672,693,700,702,720,735,750,756,805,810,897
%N A066031 Composite numbers n the sum of whose prime factors divides n, but which are not themselves powers of primes.
%C A066031 Primes and powers of primes have been excluded from the sequence because they trivially satisfy the condition "the sum of the prime factors of n divides n". Call a term of the sequence "primitive" if it is not a multiple of some previous term; for example, 70 is primitive while 60 is not. Are there infinitely many primitive terms? See A064623.
%C A066031 Intersection of A089352 and A024619. - _Michel Marcus_, Feb 03 2016
%H A066031 Charles R Greathouse IV, <a href="/A066031/b066031.txt">Table of n, a(n) for n = 1..10000</a>
%H A066031 Jean-Marie de Koninck, Florian Luca, <a href="http://dx.doi.org/10.1016/j.jnt.2007.01.010">Integers divisible by sums of powers of their prime factors</a>, Journal of Number Theory, Volume 128, Issue 3, March 2008, Pages 557-563.
%H A066031 J. Pe, <a href="http://numeratus.net/primeperfect/primeperfect.html">The Prime-perfect Numbers</a>
%e A066031 The sum of the prime factors of 70 is 2 + 5 + 7 = 14, which divides 70.
%t A066031 Select[ Range[2, 900], IntegerQ[ # / Apply[ Plus, First[ Transpose[ FactorInteger[ # ]]]]] && Mod[ #, # - EulerPhi[ # ]] != 0 & ]
%o A066031 (PARI) isok(n) = if (omega(n)<2, return(0)); my(f = factor(n)) ; (n % vecsum(f[,1])) == 0; \\ _Michel Marcus_, Feb 03 2016
%Y A066031 Cf. A024619, A089352.
%K A066031 nonn
%O A066031 1,1
%A A066031 _Joseph L. Pe_, Dec 12 2001
%E A066031 More terms from _Robert G. Wilson v_, Dec 12 2001