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

1,1

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.

Links

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

Example

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

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]]]

Crossrefs

Cf. A008472, A056524, A240453, A240454.

Sequence in context: A087551 A164076 A128509 * A043645 A043700 A111634

Adjacent sequences: A240465 A240466 A240467 * A240469 A240470 A240471

Keyword

nonn,base

Author

Michel Lagneau, Apr 06 2014

Status

approved