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

1,2

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

Links

Table of n, a(n) for n=1..75.

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).

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 *)

Crossrefs

Cf. A002113, A002385.

Sequence in context: A360269 A345423 A159303 * A337310 A001414 A134875

Adjacent sequences: A262046 A262047 A262048 * A262050 A262051 A262052

Keyword

nonn,base

Author

R. J. Mathar, Sep 09 2015

Status

approved