A263720 Palindromic numbers such that the sum of the digits equals the number of divisors.

1, 2, 11, 22, 101, 202, 444, 525, 828, 1111, 2222, 4884, 5445, 5775, 12321, 13431, 18081, 21612, 24642, 26862, 31213, 44244, 44844, 51415, 52425, 56265, 62426, 80008, 86868, 89298, 99099, 135531, 162261, 198891, 217712, 237732, 301103, 343343, 480084, 486684, 512215, 521125

Offset

1,2

Comments

Subsequence of A002113.

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

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.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Palindromic Number

Eric Weisstein's World of Mathematics, Divisor Function

Eric Weisstein's World of Mathematics, Digit Sum

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A002113, A057531.

Sequence in context: A018737 A162468 A118594 * A235609 A018351 A004642

Adjacent sequences: A263717 A263718 A263719 * A263721 A263722 A263723

Keyword

nonn,base

Author

Ilya Gutkovskiy, Oct 24 2015

Status

approved