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A210934 Sum of prime factors of prime(n)+1 (counted with multiplicity).

%I A210934 #30 May 25 2022 08:53:04
%S A210934 3,4,5,6,7,9,8,9,9,10,10,21,12,15,11,11,12,33,21,12,39,13,14,13,16,22,
%T A210934 19,13,18,24,14,18,28,16,15,25,81,45,16,34,15,22,15,99,19,16,57,17,26,
%U A210934 30,21,16,24,17,48,20,16,25,141,52,75,19,22,22,159,58,87
%N A210934 Sum of prime factors of prime(n)+1 (counted with multiplicity).
%C A210934 From an idea of _Michael B. Porter_.
%H A210934 Paolo P. Lava, <a href="/A210934/b210934.txt">Table of n, a(n) for n = 1..10000</a>
%F A210934 a(n) = A001414(A008864(n)). - _Michel Marcus_, Oct 05 2013
%e A210934 prime(8) = 19, and 19+1 = 20 = 2*2*5, so a(8) = 2+2+5 = 9.
%p A210934 with(numtheory);
%p A210934 P:=proc(i)
%p A210934 local a,k,n;
%p A210934 for n from 1 to i do
%p A210934   a:=ifactors(ithprime(n)+1)[2]; print(add(a[k][1]*a[k][2],k=1..nops(a)));
%p A210934 od; end:
%p A210934 # alternative
%p A210934 A210934 := proc(n)
%p A210934     local p,pplus,f ;
%p A210934     p := ithprime(n) ;
%p A210934     pplus := ifactors(p+1)[2] ;
%p A210934     add(op(1,f)*op(2,f),f=pplus) ;
%p A210934 end proc:
%p A210934 seq(A210934(n),n=1..300) ; # _R. J. Mathar_, May 25 2022
%Y A210934 Cf. A023508, A023514, A210936
%K A210934 nonn
%O A210934 1,1
%A A210934 _Paolo P. Lava_, Mar 30 2012