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

1,3

Links

Table of n, a(n) for n=1..50.

Formula

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

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000720, A048656, A089819, A357214.

Sequence in context: A263794 A344608 A086530 * A147402 A052551 A147096

Adjacent sequences: A357212 A357213 A357214 * A357216 A357217 A357218

Keyword

nonn,easy

Author

Clark Kimberling, Sep 24 2022

Status

approved