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

Author

Ilya Gutkovskiy, Oct 24 2015

Keywords

• nonn
• base

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.

Examples

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

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

Crossrefs

Cf. A002113, A057531.

Programs

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 *)

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