A327324 Palindromes whose number and sum of divisors are both also palindromic.

1, 2, 3, 4, 5, 7, 333, 17571, 1757571, 1787871, 5136315, 518686815, 541626145, 17575757571, 5136813186315, 5136868686315, 5806270726085, 172757272757271, 513636363636315, 17275787578757271, 17578787578787571, 17878787578787871, 51363636363636315

Offset

1,2

Comments

Numbers m such that m, A000005(m) = tau(m) and A000203(m) = sigma(m) are all in A002113.

Corresponding values of tau(a(n)): 1, 2, 2, 3, 2, 2, 6, 4, 4, 4, 8, 8, 8, 4, 8, 8, 8, 4, 8, ...

Corresponding values of sigma(a(n)): 1, 3, 4, 7, 6, 8, 494, 23432, 2343432, 2383832, ...

Intersection of A028986 and A324988.

Links

Table of n, a(n) for n=1..23.

Example

tau(333) = A000005(333) = 6; sigma(333) = A000203(333) = 494.

Mathematica

Select[Range[2*10^6], PalindromeQ[#] && PalindromeQ[DivisorSigma[0, #]] && PalindromeQ[DivisorSigma[1, #]] &] (* Amiram Eldar, Aug 31 2019 *)

Prog

(Magma) [m: m in [1..1000000] | Intseq(m, 10) eq Reverse(Intseq(m, 10)) and Intseq(NumberOfDivisors(m), 10) eq Reverse(Intseq(NumberOfDivisors(m), 10)) and Intseq(&+[d: d in Divisors(m)], 10) eq Reverse(Intseq(&+[d: d in Divisors(m)], 10))]
(PARI) ispal(n) = my(d=digits(n)); d == Vecrev(d);
isok(n) = ispal(n) && ispal(numdiv(n)) && ispal(sigma(n)); \\ Michel Marcus, Sep 02 2019

Crossrefs

Cf. A000005, A000203, A002113, A028986, A324989, A324988.

Sequence in context: A259384 A285888 A028986 * A063948 A113929 A220394

Adjacent sequences: A327321 A327322 A327323 * A327325 A327326 A327327

Keyword

nonn,base

Author

Jaroslav Krizek, Aug 30 2019

Extensions

a(20)-a(23) with the help of Daniel Suteu

Status

approved