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

Author

Jaroslav Krizek, Mar 23 2019

Keywords

• nonn
• base

Comments

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

Examples

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

Crossrefs

Cf. A000005, A002113, A069747.

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

Includes A002385, A046328 and A046329.

Programs

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))]

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 *)

PARI

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