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A175242
a(n) = the number of divisors of n that are palindromes when written in binary.
3
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
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
Sequence in context: A035228 A035164 A023588 * A355770 A225843 A327657
KEYWORD
base,nonn
AUTHOR
Leroy Quet, Mar 11 2010
EXTENSIONS
Extended by Ray Chandler, Mar 13 2010
STATUS
approved