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Sum of the palindromic primes dividing n (with repetition).
3

%I #11 Sep 05 2022 19:32:50

%S 0,2,3,4,5,5,7,6,6,7,11,7,0,9,8,8,0,8,0,9,10,13,0,9,10,2,9,11,0,10,0,

%T 10,14,2,12,10,0,2,3,11,0,12,0,15,11,2,0,11,14,12,3,4,0,11,16,13,3,2,

%U 0,12,0,2,13,12,5,16,0,4,3,14,0,12,0,2,13

%N Sum of the palindromic primes dividing n (with repetition).

%C a(p)=0 for primes p which are not in A002385.

%C The first runs of 2, 3 and 4 identical values start at a(5), a(370) and a(2776191), respectively. - _Giovanni Resta_, Sep 09 2015

%F Let n=product_i p(i)^e(i), then a(n)=sum_{i,p(i) in A002113} e(i)*p(i).

%F a(n) <= A001414(n).

%p A262049 := proc(n)

%p local a,d ;

%p a := 0 ;

%p for d in ifactors(n)[2] do

%p if isA002113(op(1,d)) then

%p a := a+op(1,d)*op(2,d) ;

%p end if;

%p end do:

%p a ;

%p end proc:

%p seq(A262049(n),n=1..120) ;

%t palQ[n_] := Block[{d = IntegerDigits@ n}, d == Reverse@ d]; {0}~Join~

%t Table[Total@ Select[Flatten[Table[#1, {#2}] & @@@ FactorInteger@ n], palQ], {n, 2, 75}] (* _Michael De Vlieger_, Sep 09 2015 *)

%t Join[{0},Table[Total[Times@@@Select[FactorInteger[n],PalindromeQ[#[[1]]]&]],{n,2,80}]] (* _Harvey P. Dale_, Sep 05 2022 *)

%Y Cf. A002113, A002385.

%K nonn,base

%O 1,2

%A _R. J. Mathar_, Sep 09 2015