A263720 - OEIS

%I #37 Aug 28 2019 16:58:23

%S 1,2,11,22,101,202,444,525,828,1111,2222,4884,5445,5775,12321,13431,

%T 18081,21612,24642,26862,31213,44244,44844,51415,52425,56265,62426,

%U 80008,86868,89298,99099,135531,162261,198891,217712,237732,301103,343343,480084,486684,512215,521125

%N Palindromic numbers such that the sum of the digits equals the number of divisors.

%C Subsequence of A002113.

%C A000005(a(n)) = A007953(a(n)).

%C The only known palindromic primes whose sum of digits equals the numbers of divisors (primes of the form 10^k + 1) are 2,11,101.

%H Chai Wah Wu, <a href="/A263720/b263720.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DivisorFunction.html">Divisor Function</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DigitSum.html">Digit Sum</a>

%e a(3) = 11, 11 is the palindromic number, digitsum(11) = 1 + 1 = 2, sigma_0(11) = 2.

%t fQ[n_] := Block[{d = IntegerDigits@ n}, And[d == Reverse@ d, Total@ d == DivisorSigma[0, n]]]; Select[Range[2^19], fQ] (* _Michael De Vlieger_, Oct 27 2015 *)

%t Select[Range[600000],PalindromeQ[#]&&Total[IntegerDigits[#]] == DivisorSigma[ 0,#]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Aug 28 2019 *)

%o (PARI) lista(nn) = {for(n=1, nn, my(d = digits(n)); if ((Vecrev(d) == d) && (numdiv(n) == sumdigits(n)), print1(n, ", ")););} \\ _Michel Marcus_, Oct 25 2015

%Y Cf. A002113, A057531.

%K nonn,base

%O 1,2

%A _Ilya Gutkovskiy_, Oct 24 2015