

A046343


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


12



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
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. 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



