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

Author

Jaroslav Krizek, Aug 30 2019

Keywords

• nonn
• base

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.

Examples

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

Crossrefs

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

Programs

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))];

Mathematica

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

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

Extensions

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