A030632 Numbers with 14 divisors.

192, 320, 448, 704, 832, 1088, 1216, 1458, 1472, 1856, 1984, 2368, 2624, 2752, 3008, 3392, 3645, 3776, 3904, 4288, 4544, 4672, 5056, 5103, 5312, 5696, 6208, 6464, 6592, 6848, 6976, 7232, 8019, 8128, 8192, 8384, 8768, 8896, 9477, 9536, 9664, 10048, 10432

Offset

1,1

Comments

Numbers of the form p^13 (A138031) or p*q^6 (A189987), where p and q are distinct primes. - R. J. Mathar, Mar 01 2010

Links

R. J. Mathar, Table of n, a(n) for n = 1..1000

Mathematica

Select[Range[15000], DivisorSigma[0, #] == 14 &]

Prog

(PARI) is(n)=numdiv(n)==14 \\ Charles R Greathouse IV, Jun 19 2016
(Python)
from sympy import primepi, primerange, integer_nthroot
def A030632(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(x//p**6) for p in primerange(integer_nthroot(x, 6)[0]+1))+primepi(integer_nthroot(x, 7)[0])-primepi(integer_nthroot(x, 13)[0])
    return bisection(f, n, n) # Chai Wah Wu, Feb 22 2025

Crossrefs

Cf. A092759.

Sequence in context: A344860 A045077 A234135 * A189987 A229361 A232940

Adjacent sequences: A030629 A030630 A030631 * A030633 A030634 A030635

Keyword

nonn,changed

Author

Jeff Burch

Status

approved