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Palindromes whose number of divisors is palindromic.
2

%I #17 Sep 08 2022 08:46:24

%S 1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99,101,111,121,131,141,151,

%T 161,171,181,191,202,212,222,232,242,262,282,292,303,313,323,333,343,

%U 353,363,373,383,393,404,424,434,454,474,484,494,505,515,535,545

%N Palindromes whose number of divisors is palindromic.

%C Numbers m such that m and A000005(m) = tau(m) are both in A002113.

%e Number of divisors of palindrome number 22 with divisors 1, 2, 11 and 22 is 4 (palindrome number).

%p ispali:= proc(n) local L; L:= convert(n,base,10); L = ListTools:-Reverse(L) end proc:

%p select(t -> ispali(t) and ispali(numtheory:-tau(t)), [$1..10000]); # _Robert Israel_, Mar 26 2019

%t Select[Range@ 600, And[PalindromeQ@ #, PalindromeQ@ DivisorSigma[0, #]] &] (* _Michael De Vlieger_, Mar 24 2019 *)

%o (Magma) [n: n in [1..1000] | Intseq(n, 10) eq Reverse(Intseq(n, 10)) and Intseq(NumberOfDivisors(n), 10) eq Reverse(Intseq(NumberOfDivisors(n), 10))]

%o (PARI) ispal(n) = my(d=digits(n)); Vecrev(d) == d;

%o isok(n) = ispal(n) && ispal(numdiv(n)); \\ _Michel Marcus_, Mar 23 2019

%Y Cf. A000005, A002113, A069747.

%Y Similar sequences for functions sigma(m) and pod(m): A028986, A324989.

%Y Includes A002385, A046328 and A046329.

%K nonn,base

%O 1,2

%A _Jaroslav Krizek_, Mar 23 2019