

A153979


Prime sums of prime factors of composite(k)=A002808(k).


1



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

1,1


COMMENTS

More precisely: Take the sum of prime factors of the nth 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
The count of the same numbers is A168470.  Gionata Neri, Apr 26 2015


LINKS

Karl Hovekamp, Table of n, a(n) for n=1,...,12285.
Karl Hovekamp, Table of n, a(n), source, factors for n=1,...,12285.


EXAMPLE

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.


MAPLE

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;
seq(A[i], i=1..N); # Robert Israel, Apr 26 2015


MATHEMATICA

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 *)


PROG

(PARI) forcomposite(c=1, 999, isprime(s=(s=factor(c))[, 1]~*s[, 2])&&print1(s", ")) \\ M. F. Hasler, May 02 2015


CROSSREFS

Cf. A000040, A002808.
Sequence in context: A033932 A144186 A246458 * A126992 A028316 A019163
Adjacent sequences: A153976 A153977 A153978 * A153980 A153981 A153982


KEYWORD

nonn


AUTHOR

JuriStepan Gerasimov, Jan 04 2009


EXTENSIONS

Corrected and edited by Karl Hovekamp, Dec 05 2009


STATUS

approved



