A357215 - OEIS

%I #10 Sep 26 2022 20:10:37

%S 0,1,3,3,7,7,15,15,15,15,31,31,63,63,63,63,127,127,255,255,255,255,

%T 511,511,511,511,511,511,1023,1023,2047,2047,2047,2047,2047,2047,4095,

%U 4095,4095,4095,8191,8191,16383,16383,16383,16383,32767,32767,32767,32767

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

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

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

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

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

%o (Python)

%o from sympy import primepi

%o def a(n): return 2**primepi(n) - 1

%o print([a(n) for n in range(1, 51)]) # _Michael S. Branicky_, Sep 24 2022

%Y Cf. A000720, A048656, A089819, A357214.

%K nonn,easy

%O 1,3

%A _Clark Kimberling_, Sep 24 2022