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A357215
a(n) = number of nonempty subsets S of {1, 2, ..., n} that contain only primes.
4
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
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Sep 24 2022
STATUS
approved