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A163508
The sum of the prime factors (with repetition) of the sum of 2 successive primes.
1
5, 6, 7, 8, 9, 10, 10, 12, 17, 12, 21, 18, 14, 13, 14, 15, 14, 14, 28, 14, 25, 14, 47, 36, 19, 24, 17, 15, 42, 16, 48, 71, 30, 16, 17, 22, 17, 21, 26, 21, 17, 38, 17, 23, 21, 48, 40, 18, 28, 23, 65, 18, 48, 131, 24, 30, 18, 141, 39, 54, 18, 19, 108, 24, 20, 18, 171, 29, 38, 24
OFFSET
1,1
LINKS
FORMULA
a(n)=A001414(A001043(n))=sopfr(p_n+p_(n+1)), p_n is n-th prime.
EXAMPLE
a(1)=5 because p_1+p_2=2+3=5, and sopfr(5)=5
a(2)=6 because p_2+p_3=3+5==2*2*2, and sopfr(8)=2+2+2=6
a(4)=8 because p_4+p_5=7+11=18=2*3*3 and sopfr(18)=2+3+3=8.
MAPLE
spf:= n -> add(t[1]*t[2], t=ifactors(n)[2]):
P:= [seq(ithprime(i), i=1..101)]:
map(spf, P[2..-1]+P[1..-2]); # Robert Israel, Nov 19 2020
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Zak Seidov, Jul 29 2009
STATUS
approved