A240468 - OEIS

%I #5 Apr 08 2014 09:18:36

%S 11,13,14,13,16,16,18,13,14,31,112,51,11,142,61,162,41,33,192,33,16,

%T 114,66,53,42,13,23,144,30,34,294,304,115,324,47,51,18,364,14,33,30,

%U 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

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

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

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

%C 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.

%H Michel Lagneau, <a href="/A240468/b240468.txt">Table of n, a(n) for n = 1..10000</a>

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

%p 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:

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

%Y Cf. A008472, A056524, A240453, A240454.

%K nonn,base

%O 1,1

%A _Michel Lagneau_, Apr 06 2014