A240468 Sum of the distinct prime divisors of the palindromes having an even number of digits.

11, 13, 14, 13, 16, 16, 18, 13, 14, 31, 112, 51, 11, 142, 61, 162, 41, 33, 192, 33, 16, 114, 66, 53, 42, 13, 23, 144, 30, 34, 294, 304, 115, 324, 47, 51, 18, 364, 14, 33, 30, 16, 210, 114, 39, 66, 51, 53, 240, 36, 50, 35, 113, 19, 117, 119, 26, 123, 125, 36, 152, 296, 16, 306, 162, 117, 20

Offset: 1

Author

Michel Lagneau, Apr 06 2014

Keywords

• nonn
• base

Comments

a(n) = Sopf(A056524(n)) = A008472(A056524(n)).

There exists a subsequence of squares such that 16, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, ...

There exists a subsequence of primes such that 11, 13, 19, 23, 31, 41, 47, 53, 59, 61, 67, 71, 73, 83, 89, 97, 109, 113, 131, 137, 139, 149,... but the subsequence of primes 17, 29, 37, 43, 101, 317, 433, 439, 487, 569,... is not included in the sequence.

Examples

			a(11) = 112 because Sopf(A056524(11)) = Sopf(1111) = A008472(1111) = 112.
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008472, A056524, A240453, A240454.

Programs

Maple

with(numtheory):for n from 1 to 100 do:x:=convert(n,base,10):n1:=nops(x): s:=sum('x[i]*10^(n1-i)', 'i'=1..n1):y:=n*10^n1+s:z:=factorset(y):n2:=nops(z):s1:=sum('z[j]', 'j'=1..n2):printf(`%d, `,s1):od:

Mathematica

Join[{11},d[n_]:=IntegerDigits[n];Rest[Total[Transpose[FactorInteger[Plus[FromDigits[Join[x=d[#],Reverse[x]]]]]][[1]]]&/@Range[100]]]