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 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 (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 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

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Last modified September 11 01:27 EDT 2024. Contains 375813 sequences. (Running on oeis4.)