A161917 - OEIS

%I #23 Mar 07 2018 11:12:34

%S 12,15,35,42,60,63,66,68,84,90,95,110,114,119,140,143,152,168,189,195,

%T 204,209,216,234,245,258,264,270,280,287,290,294,297,319,322,323,352,

%U 368,377,380,384,396,470,476,480,506,510,527,531,544,552,558,559,572

%N Numbers n for which the sum of their prime factors (with repetition) divides the sum of their divisors.

%H Carl R. White, <a href="/A161917/b161917.txt">Table of n, a(n) for n = 1..10000</a>

%F {n: A001414(n) | A000203(n)}. - _R. J. Mathar_, Jun 26 2009

%e n=12: Sum_divisors (1,2,3,4,6,12) = 28; Sum_prime_factors (2,2,3) =7 -> 28/7 = 4. n=319: Sum_divisors (1,11,29,319) = 360; Sum_prime_factors (11,29) =40 -> 360/40 = 9.

%p with(numtheory); P:=proc(q) local a,n;

%p for n from 2 to q do if not isprime(n) then a:=ifactors(n)[2];

%p if type(sigma(n)/add(a[k][1]*a[k][2],k=1..nops(a)),integer) then print(n);

%p fi; fi; od; end: P(10^4);

%t Select[Range[2,600],Divisible[DivisorSigma[1,#],Total[ Times@@@ FactorInteger[#]]]&] (* _Harvey P. Dale_, Dec 09 2010 *)

%Y Cf. A161918

%K easy,nonn

%O 1,1

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Jun 23 2009

%E Offset corrected by _R. J. Mathar_, Jun 26 2009