A093640 Number of divisors of n whose binary representation is contained in that of n.

1, 2, 2, 3, 2, 4, 2, 4, 2, 4, 2, 6, 2, 4, 3, 5, 2, 4, 2, 6, 2, 4, 2, 8, 2, 4, 3, 6, 2, 6, 2, 6, 2, 4, 2, 6, 2, 4, 3, 8, 2, 4, 2, 6, 4, 4, 2, 10, 2, 4, 3, 6, 2, 6, 4, 8, 3, 4, 2, 9, 2, 4, 4, 7, 2, 4, 2, 6, 2, 4, 2, 8, 2, 4, 4, 6, 2, 6, 2, 10, 2, 4, 2, 6, 3, 4, 3, 8, 2, 8, 3, 6, 3, 4, 3, 12, 2, 4, 3, 6, 2

Offset

1,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences related to binary expansion of n.

Formula

a(n) > 1 for n>1.

a(p) = 2 for primes p.

a(A093641(n)) = A000005(A093641(n)).

a(A093642(n)) < A000005(A093642(n)).

Example

n = 18: divisors of 18: 1 = '1', 2 = '10', 3 = '11', 6 = '110', 9 = '1001' and 18 = '10010': four of them are binary substrings of '10010', therefore a(18) = 4.

Mathematica

a[n_] := DivisorSum[n, 1 &, StringContainsQ @@ IntegerString[{n, #}, 2] &]; Array[a, 100] (* Amiram Eldar, Jul 16 2022 *)

Prog

(Haskell)
import Data.List (isInfixOf)
a093640 n  = length [d | d <- [1..n], mod n d == 0,
                         show (a007088 d) `isInfixOf` show (a007088 n)]
-- Reinhard Zumkeller, Jan 22 2012
(Python)
from sympy import divisors
def a(n):
    s = bin(n)[2:]
    return sum(1 for d in divisors(n, generator=True) if bin(d)[2:] in s)
print([a(n) for n in range(1, 102)]) # Michael S. Branicky, Jul 11 2022

Crossrefs

Cf. A000005, A078822, A007088, A093641, A093642.

Sequence in context: A157986 A025479 A079243 * A320538 A343650 A327391

Adjacent sequences: A093637 A093638 A093639 * A093641 A093642 A093643

Keyword

base,nonn

Author

Reinhard Zumkeller, Apr 07 2004

Status

approved