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

1,2

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

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000005 (d), A004086 (R), A002113 (subsequence), A085329.

Sequence in context: A289351 A362038 A171550 * A085869 A068892 A106801

Adjacent sequences: A062892 A062893 A062894 * A062896 A062897 A062898

Keyword

base,nonn,easy

Author

Amarnath Murthy, Jun 30 2001

Extensions

Corrected and extended by Vladeta Jovovic, Jun 30 2001

Status

approved