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The sum of the prime factors (with repetition) of the sum of 2 successive primes.
1

%I #8 Nov 19 2020 01:07:47

%S 5,6,7,8,9,10,10,12,17,12,21,18,14,13,14,15,14,14,28,14,25,14,47,36,

%T 19,24,17,15,42,16,48,71,30,16,17,22,17,21,26,21,17,38,17,23,21,48,40,

%U 18,28,23,65,18,48,131,24,30,18,141,39,54,18,19,108,24,20,18,171,29,38,24

%N The sum of the prime factors (with repetition) of the sum of 2 successive primes.

%H Robert Israel, <a href="/A163508/b163508.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n)=A001414(A001043(n))=sopfr(p_n+p_(n+1)), p_n is n-th prime.

%e a(1)=5 because p_1+p_2=2+3=5, and sopfr(5)=5

%e a(2)=6 because p_2+p_3=3+5==2*2*2, and sopfr(8)=2+2+2=6

%e a(4)=8 because p_4+p_5=7+11=18=2*3*3 and sopfr(18)=2+3+3=8.

%p spf:= n -> add(t[1]*t[2],t=ifactors(n)[2]):

%p P:= [seq(ithprime(i),i=1..101)]:

%p map(spf, P[2..-1]+P[1..-2]); # _Robert Israel_, Nov 19 2020

%t spf[n_]:=Total[Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[n]]]; Module[ {tsp=Total/@Partition[Prime[Range[80]],2,1]},spf/@tsp] (* _Harvey P. Dale_, Jul 12 2020 *)

%Y A001043, A001414.

%K nonn,look

%O 1,1

%A _Zak Seidov_, Jul 29 2009