A371195 List of values q^5-q^4 as q runs through A000961 (that is, 1, primes, and prime powers).

0, 16, 162, 768, 2500, 14406, 28672, 52488, 146410, 342732, 983040, 1336336, 2345778, 6156502, 9375000, 13817466, 19803868, 27705630, 32505856, 67469796, 113030440, 143589642, 224465326, 276710448, 410305012, 702806938, 830750460, 1056964608, 1329973986, 1778817670, 2044673352

Offset

1,2

Comments

Parekh et al. conjecture that q^5-q^4 is the number of nonsingular generalized Weierstrass curves over the field with q elements, for q>1.

Links

Table of n, a(n) for n=1..31.

Param Parekh, Paavan Parekh, Sourav Deb, and Manish K. Gupta, On the Classification of Weierstrass Elliptic Curves over Z_n, arXiv:2310.11768 [cs.CR], 2023.

Prog

(Python)
from sympy import primepi, integer_nthroot
def A371195(n):
    def f(x): return int(n-2+x-sum(primepi(integer_nthroot(x, k)[0]) for k in range(1, x.bit_length())))
    kmin, kmax = 1, 2
    while f(kmax) >= kmax:
        kmax <<= 1
    while True:
        kmid = kmax+kmin>>1
        if f(kmid) < kmid:
            kmax = kmid
        else:
            kmin = kmid
        if kmax-kmin <= 1:
            break
    return kmax**4*(kmax-1) # Chai Wah Wu, Aug 20 2024

Crossrefs

16*A371193 is a subsequence.

Cf. A000961.

Sequence in context: A335175 A238533 A085538 * A259547 A211558 A333062

Adjacent sequences: A371192 A371193 A371194 * A371196 A371197 A371198

Keyword

nonn

Author

N. J. A. Sloane, Mar 14 2024

Status

approved