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

Author

Morgan L. Owens, Nov 21 2014

Keywords

• nonn

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

Crossrefs

Cf. A034729, A077049, A178472.

Programs

Mathematica

With[{n=Range[100]},(1/2) ((Total/@(2^Divisors[n])) - 2^n)]

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<Chai Wah Wu, Jul 15 2022

Formula

a(n) = A034729(n) - 2^(n-1). - Michel Marcus, Nov 22 2014