A201266 The seventh divisor of numbers with exactly 49 divisors.

9, 16, 16, 27, 49, 22, 26, 81, 32, 125, 32, 81, 32, 81, 125, 81, 32, 32, 169, 81, 37, 343, 41, 289, 43, 87, 343, 93, 47, 361, 53, 111, 529, 59, 343, 61, 123, 129, 361, 64, 141, 64, 1331, 625, 64, 625, 64, 159, 529, 64, 177, 64, 183, 625, 1331, 64, 201, 64

Offset: 1

Author

Reinhard Zumkeller, Nov 29 2011

Keywords

• nonn

Examples

			a(1) = A114334(7);
a(2) = A159765(7).
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A175755, A135581.

Programs

Haskell

a201266 n = [d | d <- [1..], a175755 n `mod` d == 0] !! 6

Python

from math import isqrt
from sympy import primepi, integer_nthroot, primerange, divisors
def A201266(n):
    def bisection(f,kmin=0,kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        kmin = kmax >> 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    def f(x): return int(n+x+(t:=primepi(s:=isqrt(y:=integer_nthroot(x,6)[0])))+(t*(t-1)>>1)-sum(primepi(y//k) for k in primerange(1, s+1))-primepi(integer_nthroot(x,48)[0]))
    return divisors(bisection(f,n,n))[6] # Chai Wah Wu, Feb 22 2025