A175744 Numbers with 34 divisors.

196608, 327680, 458752, 720896, 851968, 1114112, 1245184, 1507328, 1900544, 2031616, 2424832, 2686976, 2818048, 3080192, 3473408, 3866624, 3997696, 4390912, 4653056, 4784128, 5177344, 5439488, 5832704, 6356992, 6619136, 6750208, 7012352, 7143424, 7405568

Offset

1,1

Comments

Numbers of the form p^33 and p^16*q^1, 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))=34.

Mathematica

Select[Range[6000000], DivisorSigma[0, #]==34&] (* Vladimir Joseph Stephan Orlovsky, May 06 2011 *)

Prog

(PARI) is(n)=numdiv(n)==34 \\ Charles R Greathouse IV, Jun 19 2016
(Python)
from sympy import primepi, primerange, integer_nthroot
def A175744(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-sum(primepi(x//p**16) for p in primerange(integer_nthroot(x, 16)[0]+1))+primepi(integer_nthroot(x, 17)[0])-primepi(integer_nthroot(x, 33)[0]))
    return bisection(f, n, n) # Chai Wah Wu, Feb 22 2025

Crossrefs

Cf. A175742, A175743.

Sequence in context: A034597 A037148 A323282 * A024211 A204943 A345657

Adjacent sequences: A175741 A175742 A175743 * A175745 A175746 A175747

Keyword

nonn

Author

Jaroslav Krizek, Aug 27 2010

Status

approved