A175745 Numbers with 35 divisors.

5184, 11664, 40000, 153664, 250000, 455625, 937024, 1265625, 1750329, 1827904, 1882384, 5345344, 8340544, 9529569, 10673289, 17909824, 20820969, 28344976, 37515625, 45265984, 59105344, 60886809, 73530625, 77228944, 95004009, 119946304, 143496441, 180848704

Offset

1,1

Comments

Numbers of the form p^34 and p^6*q^4 (A190464), where p and q are distinct primes.

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

OEIS Wiki, Index entries for number of divisors

Formula

A000005(a(n)) = 35.

Sum_{n>=1} 1/a(n) = P(4)*P(6) - P(10) + P(34) = 0.000320676..., where P is the prime zeta function. - Amiram Eldar, Jul 03 2022

Mathematica

Select[Range[9000000], DivisorSigma[0, #]==35&] (* Vladimir Joseph Stephan Orlovsky, May 06 2011 *)

Prog

(PARI) is(n)=numdiv(n)==35 \\ Charles R Greathouse IV, Jun 19 2016
(Python)
from sympy import primepi, integer_nthroot, primerange
def A175745(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 n+x-sum(primepi(integer_nthroot(x//p**6, 4)[0]) for p in primerange(integer_nthroot(x, 6)[0]+1))+primepi(integer_nthroot(x, 10)[0])-primepi(integer_nthroot(x, 34)[0])
    return bisection(f, n, n) # Chai Wah Wu, Feb 22 2025

Crossrefs

Cf. A000005, A175742, A175743, A175744.

Sequence in context: A186847 A185485 A061050 * A190464 A031570 A066167

Adjacent sequences: A175742 A175743 A175744 * A175746 A175747 A175748

Keyword

nonn

Author

Jaroslav Krizek, Aug 27 2010

Extensions

Extended by T. D. Noe, May 08 2011

Status

approved