cp's OEIS Frontend

A359079 a(n) is the sum of the divisors d of 2*n such that the binary expansions of d and 2*n have no common 1-bit.

%I A359079 #10 Dec 16 2022 11:52:09
%S A359079 1,3,1,7,6,6,1,15,10,13,1,16,1,3,1,31,18,33,1,32,22,3,1,36,6,3,10,14,
%T A359079 1,6,1,63,34,54,1,70,38,22,1,70,42,48,1,7,6,3,1,76,1,38,18,7,1,24,1,
%U A359079 36,1,3,1,21,1,3,1,127,84,116,1,126,70,38,1,153,74,77
%N A359079 a(n) is the sum of the divisors d of 2*n such that the binary expansions of d and 2*n have no common 1-bit.
%C A359079 Odd numbers share a 1-bit (2^0) with all their divisors, hence this sequence deals with even numbers.
%H A359079 Rémy Sigrist, <a href="/A359079/b359079.txt">Table of n, a(n) for n = 1..10000</a>
%H A359079 <a href="/index/Di#divisors">Index entries for sequences related to divisors</a>
%F A359079 a(n) <= A346878(n) with equality iff n is a power of 2.
%e A359079 For n = 6:
%e A359079 - the divisors of 12 are:
%e A359079       d   bin(d)  common bit?
%e A359079       --  ------  -----------
%e A359079        1       1  no
%e A359079        2      10  no
%e A359079        3      11  no
%e A359079        4     100  yes
%e A359079        6     110  yes
%e A359079       12    1100  yes
%e A359079 - hence a(6) = 1 + 2 + 3 = 6.
%t A359079 a[n_] := DivisorSum[2n, #*Boole[BitAnd[#, 2n] == 0] &]; Array[a, 74]
%o A359079 (PARI) a(n) = sumdiv(2*n, d, if (bitand(2*n,d)==0, d, 0))
%o A359079 (Python)
%o A359079 from sympy import divisors as divs
%o A359079 def a(n): return sum(d for d in divs(2*n, generator=True) if (d>>1)&n == 0)
%o A359079 print([a(n) for n in range(1, 75)]) # _Michael S. Branicky_, Dec 15 2022
%Y A359079 Cf. A246601, A346878.
%K A359079 nonn,base
%O A359079 1,2
%A A359079 _Rémy Sigrist_, Dec 15 2022