

A046343


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


13



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, 12, 15, 11, 25, 11, 14, 12, 20, 17, 11, 16, 13, 22, 31, 12, 33, 13, 12, 18, 16, 21, 26, 14, 12, 39, 13, 23, 18, 18, 13, 12, 43, 14, 22, 45, 32, 17, 13, 20, 27, 34, 49, 24, 13, 16, 17
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OFFSET

1,1


COMMENTS

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


LINKS



FORMULA



EXAMPLE

a(31)=25 because 46 = 2 * 23 and 25 = 2 + 23.


MAPLE

count:= 0:
for n from 2 while count < 200 do
if not isprime(n) then
count:= count+1;
a[count]:= add(t[1]*t[2], t=ifactors(n)[2])
fi
od:


MATHEMATICA

Total@ Flatten[Table[#1, {#2}] & @@@ FactorInteger@ #] & /@ Select[Range@ 120, CompositeQ] (* Michael De Vlieger, Jun 11 2015 *)
t = {}; Do[If[! PrimeQ[n], AppendTo[t, Apply[Dot, Transpose[FactorInteger[n]]]]], {n, 4, 245}]; t (* Zak Seidov, Jul 03 2015 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



