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A247146
As a binary numeral, the bit 2^(m-1) of a(n) is 1 iff m is a proper divisor of n.
2
0, 1, 1, 3, 1, 7, 1, 11, 5, 19, 1, 47, 1, 67, 21, 139, 1, 295, 1, 539, 69, 1027, 1, 2223, 17, 4099, 261, 8267, 1, 16951, 1, 32907, 1029, 65539, 81, 133423, 1, 262147, 4101, 524955, 1, 1056871, 1, 2098187, 16661, 4194307, 1, 8423599, 65, 16777747, 65541
OFFSET
1,4
COMMENTS
a(n)==1 iff n is prime.
Apparently Moebius transform of A178472.
For n>1, the binary representation of a(n) is given by row (n-1) of A077049 (when read as a triangular array). - Tom Edgar, Nov 28 2014
FORMULA
a(n) = A034729(n) - 2^(n-1). - Michel Marcus, Nov 22 2014
MATHEMATICA
With[{n=Range[100]}, (1/2) ((Total/@(2^Divisors[n])) - 2^n)]
PROG
(PARI) a(n) = sumdiv(n, k, 2^(k-1)) - 2^(n-1); \\ Michel Marcus, Nov 25 2014
(Python)
from sympy import divisors
def A247146(n): return sum(1<<d-1 for d in divisors(n, generator=True) if d<n) # Chai Wah Wu, Jul 15 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Morgan L. Owens, Nov 21 2014
STATUS
approved