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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
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.
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.
Sequence in context: A167294 A304439 A266537 * A285782 A285538 A293935
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 15 2019
STATUS
approved