cp's OEIS Frontend

A328337 The number whose binary indices are the nontrivial divisors of n (greater than 1 and less than n).

%I A328337 #14 Jul 15 2022 02:31:44
%S A328337 0,0,0,2,0,6,0,10,4,18,0,46,0,66,20,138,0,294,0,538,68,1026,0,2222,16,
%T A328337 4098,260,8266,0,16950,0,32906,1028,65538,80,133422,0,262146,4100,
%U A328337 524954,0,1056870,0,2098186,16660,4194306,0,8423598,64,16777746,65540
%N A328337 The number whose binary indices are the nontrivial divisors of n (greater than 1 and less than n).
%C A328337 A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.
%F A328337 A000120(a(n)) = A070824(n).
%F A328337 A070939(a(n)) = A032742(n).
%F A328337 A001511(a(n)) = A107286(n).
%e A328337 The nontrivial divisors of 18 are {2, 3, 6, 9}, so a(18) = 2^1 + 2^2 + 2^5 + 2^8 = 294.
%t A328337 Table[Total[(2^DeleteCases[Divisors[n],1|n])/2],{n,100}]
%o A328337 (Python)
%o A328337 from sympy import divisors
%o A328337 def A328337(n): return sum(1<<(d-1) for d in divisors(n,generator=True) if 1<d<n) # _Chai Wah Wu_, Jul 15 2022
%Y A328337 Removing zeros gives binary indices of rows of A163870.
%Y A328337 The version for all divisors is A034729.
%Y A328337 The version for proper divisors is A247146.
%Y A328337 Cf. A000005, A000120, A027750, A029931, A033676, A048793, A060775, A070824, A070939, A275700, A326031.
%K A328337 nonn
%O A328337 1,4
%A A328337 _Gus Wiseman_, Oct 15 2019