A175242 a(n) = the number of divisors of n that are palindromes when written in binary.

1, 1, 2, 1, 2, 2, 2, 1, 3, 2, 1, 2, 1, 2, 4, 1, 2, 3, 1, 2, 4, 1, 1, 2, 2, 1, 4, 2, 1, 4, 2, 1, 3, 2, 3, 3, 1, 1, 2, 2, 1, 4, 1, 1, 6, 1, 1, 2, 2, 2, 4, 1, 1, 4, 2, 2, 2, 1, 1, 4, 1, 2, 6, 1, 3, 3, 1, 2, 2, 3, 1, 3, 2, 1, 4, 1, 2, 2, 1, 2, 4, 1, 1, 4, 4, 1, 2, 1, 1, 6, 2, 1, 4, 1, 2, 2, 1, 2, 5, 2, 1, 4, 1, 1, 6

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A244162 = 2.378795... . - Amiram Eldar, Jan 01 2024

Example

a(3) = 2 since 3 has 2 divisors, 1 and 3, that are palindromes when written in binary: 1 and 11.

Maple

a:= n-> add(`if`(l=ListTools[Reverse](l), 1, 0), l=
        map(Bits[Split], numtheory[divisors](n))):
seq(a(n), n=1..105);  # Alois P. Heinz, Jul 15 2022

Mathematica

palbQ[n_]:=Module[{idn2=IntegerDigits[n, 2]}, idn2==Reverse[idn2]]; Table[ Count[ Divisors[ n], _?(palbQ[#]&)], {n, 110}] (* Harvey P. Dale, Mar 27 2019 *)
a[n_] := DivisorSum[n, 1 &, PalindromeQ @ IntegerDigits[#, 2] &]; Array[a, 100] (* Amiram Eldar, Jan 01 2020 *)

Prog

(PARI) is(n) = my(d=binary(n)); d==Vecrev(d); \\ A006995
a(n) = sumdiv(n, d, is(d)); \\ Michel Marcus, Jul 15 2022
(Python)
from sympy import divisors
def c(n): b = bin(n)[2:]; return b == b[::-1]
def a(n): return sum(1 for d in divisors(n, generator=True) if c(d))
print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Jul 15 2022

Crossrefs

Cf. A006995, A244162.

Sequence in context: A035228 A035164 A023588 * A355770 A225843 A327657

Adjacent sequences: A175239 A175240 A175241 * A175243 A175244 A175245

Keyword

base,nonn

Author

Leroy Quet, Mar 11 2010

Extensions

Extended by Ray Chandler, Mar 13 2010

Status

approved