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reviewed
approved
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Revision History for A036454
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Prime powers with special exponents: q^(p-1) where p > 2 and q are prime numbers.
(history; published version)
(history; published version)
STATUS
proposed
reviewed
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editing
proposed
PROG
return bisection(f, n, n) # Chai Wah Wu, Sep 12 2024
PROG
(Python)
from sympy import primepi, integer_nthroot, primerange
def A036454(n):
def f(x): return int(n+x-sum(primepi(integer_nthroot(x, p-1)[0]) for p in primerange(3, x.bit_length()+1)))
def bisection(f, kmin=0, kmax=1):
while f(kmax) > kmax: kmax <<= 1
while kmax-kmin > 1:
kmid = kmax+kmin>>1
if f(kmid) <= kmid:
kmax = kmid
else:
kmin = kmid
return kmax
return bisection(f, n, n) # Chai Wah Wu, Sep 12 2024
STATUS
approved
editing
STATUS
reviewed
approved
STATUS
proposed
reviewed
STATUS
editing
proposed
FORMULA
Sum_{n>=1} 1/a(n) = Sum_{k>=2} P(prime(k)-1) = 0.54756961912815344341..., where P is the prime zeta function. - Amiram Eldar, Jul 10 2022
STATUS
approved
editing
STATUS
reviewed
approved