A163508 The sum of the prime factors (with repetition) of the sum of 2 successive primes.

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

A001043, A001414.

Sequence in context: A217293 A201971 A169869 * A168095 A030541 A020710

Adjacent sequences: A163505 A163506 A163507 * A163509 A163510 A163511

Keyword

nonn,look

Author

Zak Seidov, Jul 29 2009

Status

approved