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

1,4

Comments

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.

Links

Table of n, a(n) for n=1..51.

Formula

A000120(a(n)) = A070824(n).

A070939(a(n)) = A032742(n).

A001511(a(n)) = A107286(n).

Example

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

Mathematica

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

Prog

(Python)
from sympy import divisors
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

Crossrefs

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.

Sequence in context: A167294 A304439 A266537 * A285782 A285538 A293935

Adjacent sequences: A328334 A328335 A328336 * A328338 A328339 A328340

Keyword

nonn

Author

Gus Wiseman, Oct 15 2019

Status

approved