|
|
A328337
|
|
The number whose binary indices are the nontrivial divisors of n (greater than 1 and less than n).
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
FORMULA
|
|
|
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.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|