A247146 -id:A247146 - cp's OEIS frontend

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

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, 4098, 260, 8266, 0, 16950, 0, 32906, 1028, 65538, 80, 133422, 0, 262146, 4100, 524954, 0, 1056870, 0, 2098186, 16660, 4194306, 0, 8423598, 64, 16777746, 65540

Offset: 1

Gus Wiseman, Oct 15 2019

nonn

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.

			The nontrivial divisors of 18 are {2, 3, 6, 9}, so a(18) = 2^1 + 2^2 + 2^5 + 2^8 = 294.

Removing zeros gives binary indices of rows of A163870.
The version for all divisors is A034729.
The version for proper divisors is A247146.
Cf. A000005, A000120, A027750, A029931, A033676, A048793, A060775, A070824, A070939, A275700, A326031.

Table[Total[(2^DeleteCases[Divisors[n],1|n])/2],{n,100}]

from sympy import divisors
def A328337(n): return sum(1<<(d-1) for d in divisors(n,generator=True) if 1Chai Wah Wu, Jul 15 2022

A000120(a(n)) = A070824(n).
A070939(a(n)) = A032742(n).
A001511(a(n)) = A107286(n).

cp's OEIS Frontend

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

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