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A325307 a(n) = k / (sum of prime factors of k, counted with multiplicity) where k is the n-th number for which the ratio is an integer.

%I A325307 #33 Mar 24 2023 23:12:23
%S A325307 1,1,1,1,1,1,1,2,1,1,1,3,1,3,1,1,1,1,1,1,1,5,1,1,5,1,6,1,1,1,6,1,1,1,
%T A325307 1,7,1,1,1,1,1,1,1,1,10,1,1,1,1,1,1,12,1,1,1,1,1,1,11,1,1,1,11,1,1,15,
%U A325307 1,1,16,1,1,1,1,1,1,1,11,18,1,1,14,1,1,1,1,1,1,1,1,1,1,1,21,1,1,1,1,1,1,1,1,1,1,1,20,1,1,25
%N A325307 a(n) = k / (sum of prime factors of k, counted with multiplicity) where k is the n-th number for which the ratio is an integer.
%H A325307 Robert Israel, <a href="/A325307/b325307.txt">Table of n, a(n) for n = 1..10000</a>
%e A325307 a(8) = 2 comes from k = A036844(8) = 16 = 2^4. The sum of prime factors is 2 + 2 + 2 + 2 = 8, so k/(sum of prime factors of k) = 2.
%p A325307 Res:= NULL: count:= 0:
%p A325307 for n from 2 while count < 200 do
%p A325307   F:= ifactors(n)[2];
%p A325307   r:= n /add(t[1]*t[2],t=F);
%p A325307   if r::integer then count:= count+1; Res:= Res, r fi
%p A325307 od:
%p A325307 Res; # _Robert Israel_, Jul 29 2019
%t A325307 Select[Array[#/Total@ Flatten[ConstantArray[#1, #2] & @@ # & /@ FactorInteger[#]] &, 450, 2], IntegerQ] (* _Michael De Vlieger_, Apr 21 2019 *)
%o A325307 (Python)
%o A325307 maxNum = 455
%o A325307 ratios = []
%o A325307 for i in range(2, maxNum):
%o A325307   sumFactors = A001414(i)
%o A325307   if i % sumFactors == 0:
%o A325307     ratio = i // sumFactors
%o A325307     ratios.append(ratio)
%o A325307 print(ratios) # ratios is an array that contains the sequence
%Y A325307 Cf. A001414 (sum of prime factors), A036844 (values of k).
%K A325307 nonn
%O A325307 1,8
%A A325307 _Sven Kunze_, Apr 20 2019