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

1,1

Links

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

Example

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

Prog

(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

Crossrefs

Cf. A175755, A135581.

Sequence in context: A131746 A092095 A186851 * A231977 A269563 A217570

Adjacent sequences: A201263 A201264 A201265 * A201267 A201268 A201269

Keyword

nonn

Author

Reinhard Zumkeller, Nov 29 2011

Status

approved