A153979 Prime sums of prime factors of composite(k)=A002808(k).

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

Offset: 1

Author

Juri-Stepan Gerasimov, Jan 04 2009

Keywords

• nonn

Comments

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

The count of the same numbers is A168470. - Gionata Neri, Apr 26 2015

Examples

			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.
		

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.

Crossrefs

Cf. A000040, A002808.

Programs

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 *)

PARI

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

Extensions

Corrected and edited by Karl Hovekamp, Dec 05 2009