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A240468
Sum of the distinct prime divisors of the palindromes having an even number of digits.
1
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
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
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Apr 06 2014
STATUS
approved