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A246600 Number of divisors d of n with property that the binary representation of d can be obtained from the binary representation of n by changing any number of 1's to 0's. 2
1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 4, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 4, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 4, 2, 2, 4, 3, 2, 2, 2, 2, 4, 2, 2, 6, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 4, 2, 3, 2, 2, 4, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Equivalently, the number of divisors d of n such that the bitwise OR of n and d is equal to n. - Chai Wah Wu, Sep 06 2014

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

FORMULA

a(2^i) = 1.

a(odd prime) = 2.

a(n) <= 2^wt(n)-1, where wt(n) = A000120(n).

a(n) = Sum_{d|n} (binomial(n,d) mod 2). - Ridouane Oudra, May 03 2019

EXAMPLE

12 = 1100_2; only the divisors 4 = 0100_2 and 12 = 1100_2 satisfy the condition, so(12)=2.

15 = 1111_2; all divisors 1,3,5,15 satisfy the condition, so a(15)=4.

MAPLE

with(numtheory);

sd:=proc(n) local a, d, s, t, i, sw;

s:=convert(n, base, 2);

a:=0;

for d in divisors(n) do

sw:=-1;

t:=convert(d, base, 2);

for i from 1 to nops(t) do if t[i]>s[i] then sw:=1; fi; od:

if sw<0 then a:=a+1; fi;

od;

a;

end;

[seq(sd(n), n=1..100)];

MATHEMATICA

a[n_] := DivisorSum[n, Boole[BitOr[#, n] == n]&]; Array[a, 100] (* Jean-Fran├žois Alcover, Dec 02 2015, adapted from PARI *)

PROG

(Python)

from sympy import divisors

def A246600(n):

....return sum(1 for d in divisors(n) if n|d == n)

# Chai Wah Wu, Sep 06 2014

(PARI) a(n)=sumdiv(n, d, bitor(d, n)==n) \\ Charles R Greathouse IV, Sep 29 2014

CROSSREFS

Cf. A000005, A000120, A246601.

Sequence in context: A254315 A080942 A099812 * A068068 A193523 A092505

Adjacent sequences:  A246597 A246598 A246599 * A246601 A246602 A246603

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Sep 06 2014

STATUS

approved

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Last modified March 8 13:59 EST 2021. Contains 341949 sequences. (Running on oeis4.)