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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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A206291 A058979 A225491 * A273227 A319500 A022911
KEYWORD
nonn
AUTHOR
Patrick De Geest, Jun 15 1998
STATUS
approved

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Last modified March 18 22:47 EDT 2024. Contains 370951 sequences. (Running on oeis4.)