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A263720
Palindromic numbers such that the sum of the digits equals the number of divisors.
1
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
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
Sequence in context: A018737 A162468 A118594 * A235609 A376688 A018351
KEYWORD
nonn,base
AUTHOR
Ilya Gutkovskiy, Oct 24 2015
STATUS
approved