A262049 Sum of the palindromic primes dividing n (with repetition).

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

Offset: 1

Author

R. J. Mathar, Sep 09 2015

Keywords

• nonn
• base

Comments

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

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

Crossrefs

Cf. A002113, A002385.

Programs

Maple

A262049 := proc(n)
    local a,d ;
    a := 0 ;
    for d in ifactors(n)[2] do
        if isA002113(op(1,d)) then
            a := a+op(1,d)*op(2,d) ;
        end if;
    end do:
    a ;
end proc:
seq(A262049(n),n=1..120) ;

Mathematica

palQ[n_] := Block[{d = IntegerDigits@ n}, d == Reverse@ d]; {0}~Join~
Table[Total@ Select[Flatten[Table[#1, {#2}] & @@@ FactorInteger@ n], palQ], {n, 2, 75}] (* Michael De Vlieger, Sep 09 2015 *)
Join[{0},Table[Total[Times@@@Select[FactorInteger[n],PalindromeQ[#[[1]]]&]],{n,2,80}]] (* Harvey P. Dale, Sep 05 2022 *)

Formula

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

a(n) <= A001414(n).