A337769 -id:A337769 - cp's OEIS frontend

A353024 Largest k such that A007504(k) <= n^2.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 10, 11, 11, 12, 13, 14, 14, 15, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 23, 23, 24, 25, 25, 26, 27, 27, 28, 29, 30, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 37, 37, 38, 39, 39, 40, 40, 41, 42, 42, 43, 44, 44, 45, 45, 46, 47, 47

Offset: 1

Joelle H. Kassir, Apr 17 2022

nonn

Cf. A000290, A007504, A337769, A350174, A033997.

first(N)=my(v=vector(N),s,k,n=1,n2=1); forprime(p=2,, s+=p; k++; while(s>n2, v[n]=k-1; if(n++>N, return(v)); n2=n^2)) \\ Charles R Greathouse IV, Apr 18 2022

a(n)=my(n2=n^2,s,k); forprime(p=2,, s+=p; k++; if(s>n2, return(k-1))) \\ Charles R Greathouse IV, Apr 18 2022

from sympy import prime
def a(n):
    k = 1
    total = 0
    while True:
        total += prime(k)
        if total > n**2:
            break
        k += 1
    return k-1

a(n) = A337769(n) - 1.
a(n) ~ sqrt(2)*n/sqrt(log n). - Charles R Greathouse IV, Apr 18 2022
a(n) = A350174(n^2). - Kevin Ryde, Apr 19 2022

A356593 Smallest k such that primorial(k) > n^2.

Original entry on oeis.org

1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

Offset: 1

Christoph B. Kassir, Aug 14 2022

nonn

Cf. A337769, A002110, A000290.

a[n_] := Module[{k = 1, prod = p = 2}, While[prod < n^2, p = NextPrime[p]; prod *= p; k++]; k]; Array[a, 100] (* Amiram Eldar, Aug 15 2022 *)

from sympy import primorial
def a(n):
    k = 1
    while True:
        if primorial(k) > n**2:
            return(k)
        k += 1
for n in range(1, 90):
    print(f'{a(n)}, ', end='')

cp's OEIS Frontend

A353024 Largest k such that A007504(k) <= n^2.

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