A062895 Numbers k for which d(k) = d(R(k)), where R(k) is the reversal of k and d(k) is the number of divisors of k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 15, 17, 22, 24, 26, 31, 33, 37, 39, 42, 44, 51, 55, 58, 62, 66, 71, 73, 77, 79, 85, 88, 93, 97, 99, 101, 107, 111, 113, 115, 117, 121, 122, 123, 129, 131, 141, 143, 149, 151, 155, 157, 158, 159, 161, 165, 167, 169, 171, 177, 178, 179

Offset: 1

Author

Amarnath Murthy, Jun 30 2001

Keywords

• base
• nonn
• easy

Comments

The sequence s of numbers k for which R(d(k)) = d(R(k)) first differs at s(80) = 262 while a(80) = 252. - Mohammed Yaseen, Mar 24 2023

Examples

			d(24) = 8 and also d(42) = 8, hence both are members.
		

Links

• Mohammed Yaseen, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)

Crossrefs

Cf. A000005 (d), A004086 (R), A002113 (palindromes: subsequence).

Cf. A350867 (subsequence of non-palindromic terms), A085329 (similar with sigma).

Programs

Mathematica

Select[Range[180],DivisorSigma[0,#]==DivisorSigma[0,FromDigits[Reverse[IntegerDigits[#]]]] &] (* Jayanta Basu, May 17 2013 *)

PARI

{ n=0; for (m=1, 10^9, x=m; r=0; while (x>0, d=x-10*(x\10); x\=10; r=r*10 + d); if (numdiv(m) == numdiv(r), write("b062895.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 12 2009

PARI

isok(k) = numdiv(fromdigits(Vecrev(digits(k)))) == numdiv(k); \\ Michel Marcus, Jul 06 2021

Python

from sympy import divisor_count as d
def ok(n): return d(n) == d(int(str(n)[::-1]))
print([k for k in range(1, 180) if ok(k)]) # Michael S. Branicky, Mar 24 2023

Extensions

Corrected and extended by Vladeta Jovovic, Jun 30 2001