A247146 As a binary numeral, the bit 2^(m-1) of a(n) is 1 iff m is a proper divisor of n.

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

Links

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

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

Cf. A034729, A077049, A178472.

Sequence in context: A273013 A050521 A266724 * A362628 A225561 A098093

Adjacent sequences: A247143 A247144 A247145 * A247147 A247148 A247149

Keyword

nonn

Author

Morgan L. Owens, Nov 21 2014

Status

approved