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

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

Offset: 1

Author

Patrick De Geest, Jun 15 1998

Keywords

• nonn

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

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

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002808, A001414.

Cf. A000607, A046344, A046345.

Programs

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:
seq(a[i],i=1..count); # Robert Israel, Jun 11 2015

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 *)

Formula

a(n) = A001414(A002808(n)). - Michel Marcus, Jun 11 2015