A093640 - OEIS

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

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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:]