A377028 a(n) = number of integers k <= n such that k is a term in A055932.

1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17

Offset

1,2

Comments

Sequence counts the number of k <= n such that the squarefree kernel of k = rad(k) = A007947(k) is a primorial number (a term in A002110). Similar counting function to A000720 (number of primes <= n).

Links

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

Example

a(30) = 10 because there are 10 numbers k <= 30 which are terms in A005932 (namely : 1,2,4,6,8,12,16,18,24,30).

Mathematica

c = 0; fQ[x_] := Or[IntegerQ@ Log2[x], And[EvenQ[x], Union@ Differences@ PrimePi[FactorInteger[x][[All, 1]] ] == {1}] ]; Reap[Do[If[fQ[n], c++]; Sow[c], {n, 10^4}] ][[-1, 1]] (* Michael De Vlieger, Oct 13 2024 *)

Prog

(Python)
from itertools import count
from functools import lru_cache
from sympy import prime, integer_log, primorial
def A377028(n):
    @lru_cache(maxsize=None)
    def g(x, m): return sum(g(x//(prime(m)**i), m-1) for i in range(1, integer_log(x, prime(m))[0]+1)) if m-1 else x.bit_length()-1
    c = 1
    for k in count(1):
        if primorial(k)>n:
            break
        c += g(n, k)
    return c # Chai Wah Wu, Mar 18 2026

Crossrefs

Cf. A000720, A002110, A007947, A055932, A376690.

Sequence in context: A228720 A219652 A069924 * A392987 A225559 A383278

Adjacent sequences: A377025 A377026 A377027 * A377029 A377030 A377031

Keyword

nonn

Author

David James Sycamore, Oct 13 2024

Extensions

More terms from Michael De Vlieger, Oct 13 2024

Status

approved