A324988 Palindromes whose number of divisors is palindromic.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 262, 282, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 404, 424, 434, 454, 474, 484, 494, 505, 515, 535, 545

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..57.

Example

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

Maple

ispali:= proc(n) local L; L:= convert(n, base, 10); L = ListTools:-Reverse(L) end proc:
select(t -> ispali(t) and ispali(numtheory:-tau(t)), [$1..10000]); # Robert Israel, Mar 26 2019

Mathematica

Select[Range@ 600, And[PalindromeQ@ #, PalindromeQ@ DivisorSigma[0, #]] &] (* Michael De Vlieger, Mar 24 2019 *)

Prog

(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))]
(PARI) ispal(n) = my(d=digits(n)); Vecrev(d) == d;
isok(n) = ispal(n) && ispal(numdiv(n)); \\ Michel Marcus, Mar 23 2019

Crossrefs

Cf. A000005, A002113, A069747.

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

Includes A002385, A046328 and A046329.

Sequence in context: A227858 A335779 A240601 * A276354 A084982 A110785

Adjacent sequences: A324985 A324986 A324987 * A324989 A324990 A324991

Keyword

nonn,base

Author

Jaroslav Krizek, Mar 23 2019

Status

approved