A175747 Numbers with 38 divisors.

786432, 1310720, 1835008, 2883584, 3407872, 4456448, 4980736, 6029312, 7602176, 8126464, 9699328, 10747904, 11272192, 12320768, 13893632, 15466496, 15990784, 17563648, 18612224, 19136512, 20709376, 21757952, 23330816, 25427968, 26476544, 27000832, 28049408

Offset: 1

Author

Jaroslav Krizek, Aug 27 2010

Keywords

• nonn

Comments

Numbers of the forms p^37 and p^18*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

Crossrefs

Cf. A175745, A175746, A139572.

Programs

Mathematica

Select[Range[10000000],DivisorSigma[0,#]==38&] (* Vladimir Joseph Stephan Orlovsky, May 06 2011 *)

PARI

is(n)=numdiv(n)==38 \\ Charles R Greathouse IV, Jun 19 2016

Python

def A175747(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**18) for p in primerange(integer_nthroot(x,18)[0]+1))+primepi(integer_nthroot(x,19)[0])-primepi(integer_nthroot(x,37)[0]))
    return bisection(f,n,n) # Chai Wah Wu, Feb 22 2025

Formula

A000005(a(n))=38.

Extensions

Extended by T. D. Noe, May 08 2011