A357215 a(n) = number of nonempty subsets S of {1, 2, ..., n} that contain only primes.

0, 1, 3, 3, 7, 7, 15, 15, 15, 15, 31, 31, 63, 63, 63, 63, 127, 127, 255, 255, 255, 255, 511, 511, 511, 511, 511, 511, 1023, 1023, 2047, 2047, 2047, 2047, 2047, 2047, 4095, 4095, 4095, 4095, 8191, 8191, 16383, 16383, 16383, 16383, 32767, 32767, 32767, 32767

Offset: 1

Author

Clark Kimberling, Sep 24 2022

Keywords

• nonn
• easy

Examples

			The nonempty subsets S of {1, 2, 3, 4} that contain only primes are these: {2}, {3}, {2,3}, thus, a(4) = 3.
		

Crossrefs

Cf. A000720, A048656, A089819, A357214.

Programs

Mathematica

Table[-1 + 2^PrimePi[n], {n, 1, 70}]

Python

from sympy import primepi
def a(n): return 2**primepi(n) - 1
print([a(n) for n in range(1, 51)]) # Michael S. Branicky, Sep 24 2022

Formula

a(n) = -1 + A048656(n).

a(n) = 2^A000720(n) - 1.