A324989 -id:A324989 - cp's OEIS frontend

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

Jaroslav Krizek, Mar 23 2019

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

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

Cf. A000005, A002113, A069747.
Similar sequences for functions sigma(m) and pod(m): A028986, A324989.
Includes A002385, A046328 and A046329.

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

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

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

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

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

Original entry on oeis.org

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

Jaroslav Krizek, Aug 30 2019

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.

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

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

[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))];

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

ispal(n) = my(d=digits(n)); d == Vecrev(d);
isok(n) = ispal(n) && ispal(numdiv(n)) && ispal(sigma(n)); \\ Michel Marcus, Sep 02 2019

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

cp's OEIS Frontend

A324988 Palindromes whose number of divisors is palindromic.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Magma

Maple

Mathematica

PARI