A378905 a(n) is the number of odd squarefree semiprimes (A046388) < prime(n).

0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 4, 5, 5, 5, 6, 8, 8, 9, 10, 10, 11, 11, 13, 16, 16, 16, 16, 16, 17, 20, 21, 22, 22, 25, 25, 26, 28, 28, 28, 29, 29, 32, 32, 32, 32, 36, 41, 41, 41, 41, 43, 43, 45, 46, 47, 49, 49, 49, 49, 49, 51, 56, 57, 57, 57, 62, 63, 65, 65, 65, 66

Offset

1,9

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

a(11) = 2 because 15 and 21 are the 2 terms of A046388 < prime(11) = 31;
a(12) = 4: 2 additional terms 33 and 35 of A046388 are < prime(12) = 37.

Mathematica

nn = 360; c = 0; n = 1; {0}~Join~Reap[Until[n > nn, If[And[SquareFreeQ[n], PrimeNu[n] == 2], c++]; If[PrimeQ[n], Sow[c]]; n += 2] ][[-1, 1]] (* Michael De Vlieger, Dec 22 2024 *)

Prog

(Python)
from math import isqrt
from sympy import primepi, prime, primerange
def A378905(n): return 0 if n<3 else int(1-((t:=primepi(s:=isqrt(p:=prime(n))))*(t+1)>>1)+sum(primepi(p//k) for k in primerange(3, s+1))) # Chai Wah Wu, Dec 22 2024

Crossrefs

Cf. A000720, A046388, A292785.

Sequence in context: A122385 A035002 A032578 * A351976 A035659 A008282

Adjacent sequences: A378902 A378903 A378904 * A378906 A378907 A378908

Keyword

nonn

Author

Hugo Pfoertner, Dec 22 2024

Status

approved