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A046343 Sum of the prime factors of the composite numbers (counted with multiplicity).

%I A046343 #20 Nov 15 2023 11:53:36
%S A046343 4,5,6,6,7,7,9,8,8,8,9,10,13,9,10,15,9,11,10,10,14,19,12,10,21,16,11,
%T A046343 12,15,11,25,11,14,12,20,17,11,16,13,22,31,12,33,13,12,18,16,21,26,14,
%U A046343 12,39,13,23,18,18,13,12,43,14,22,45,32,17,13,20,27,34,49,24,13,16,17
%N A046343 Sum of the prime factors of the composite numbers (counted with multiplicity).
%C A046343 The number of partitions of k into prime parts smaller than itself gives the number of times that a(n) = k. - _Gionata Neri_, Jun 11 2015
%C A046343 That number of partitions is A000607(k) if k is not prime, and A000607(k) - 1 if k is prime. - _Robert Israel_, Jun 11 2015
%H A046343 Robert Israel, <a href="/A046343/b046343.txt">Table of n, a(n) for n = 1..10000</a>
%F A046343 a(n) = A001414(A002808(n)). - _Michel Marcus_, Jun 11 2015
%e A046343 a(31)=25 because 46 = 2 * 23 and 25 = 2 + 23.
%p A046343 count:= 0:
%p A046343 for n from 2 while count < 200 do
%p A046343   if not isprime(n) then
%p A046343     count:= count+1;
%p A046343     a[count]:= add(t[1]*t[2],t=ifactors(n)[2])
%p A046343   fi
%p A046343 od:
%p A046343 seq(a[i],i=1..count); # _Robert Israel_, Jun 11 2015
%t A046343 Total@ Flatten[Table[#1, {#2}] & @@@ FactorInteger@ #] & /@ Select[Range@ 120, CompositeQ] (* _Michael De Vlieger_, Jun 11 2015 *)
%t A046343 t = {}; Do[If[! PrimeQ[n], AppendTo[t, Apply[Dot, Transpose[FactorInteger[n]]]]], {n, 4, 245}]; t (* _Zak Seidov_, Jul 03 2015 *)
%Y A046343 Cf. A002808, A001414.
%Y A046343 Cf. A000607, A046344, A046345.
%K A046343 nonn
%O A046343 1,1
%A A046343 _Patrick De Geest_, Jun 15 1998