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A153979
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Prime sums of prime factors of composite(k)=A002808(k).
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1
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5, 7, 7, 13, 11, 19, 11, 11, 11, 17, 11, 13, 31, 13, 13, 23, 13, 43, 17, 13, 13, 17, 19, 13, 19, 61, 23, 73, 17, 41, 23, 19, 47, 17, 19, 29, 19, 103, 29, 17, 109, 17, 19, 37, 17, 17, 71, 23, 139, 37, 19, 43, 151, 17, 83, 17, 23, 47, 43, 31, 19, 181, 17, 31, 47, 53, 193, 17, 23, 101, 23, 199, 29, 17
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OFFSET
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1,1
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COMMENTS
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More precisely: Take the sum of prime factors of the n-th composite number A002808(n), with repetition (e.g., 72 = 2^3*3^2 => 2+2+2+3+3). If the sum is prime, list it here; if not, don't list it and skip over to the next composite number. - M. F. Hasler, May 02 2015
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LINKS
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EXAMPLE
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A002808(1)=4=2*2, and 2+2=4(nonprime), so 4 does not contribute to this sequence. A002808(2)=6=2*3 and 2+3=5(prime), so a(1)=5. A002808(5)=10=2*5 and 2+5=7(prime), so a(2)=7. A002808(6)=12=2*2*3 and 2+2+3=7(prime), so a(3)=7.
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MAPLE
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N:= 1000: # to get a(1) to a(N)
count:= 0:
for x from 2 while count < N do
if not isprime(x) then
y:= add(f[1]*f[2], f=ifactors(x)[2]);
if isprime(y) then
count:= count+1;
A[count]:= y;
fi
fi
od;
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MATHEMATICA
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lim = 410; s = Select[Range@ lim, CompositeQ]; f[n_] := Plus @@ (Flatten[Table[#1, {#2}] & @@@ FactorInteger@ n]); Select[f /@ s, PrimeQ] (* Michael De Vlieger, Apr 26 2015 *)
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PROG
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(PARI) forcomposite(c=1, 999, isprime(s=(s=factor(c))[, 1]~*s[, 2])&&print1(s", ")) \\ M. F. Hasler, May 02 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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