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

1,1

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

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

Links

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

Formula

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

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:
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 *)

Crossrefs

Cf. A002808, A001414.

Cf. A000607, A046344, A046345.

Sequence in context: A206291 A058979 A225491 * A273227 A319500 A022911

Adjacent sequences: A046340 A046341 A046342 * A046344 A046345 A046346

Keyword

nonn

Author

Patrick De Geest, Jun 15 1998

Status

approved