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

1,1

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

Formula

A000005(a(n))=38.

Mathematica

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

Prog

(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

Crossrefs

Cf. A175745, A175746, A139572.

Sequence in context: A205261 A392078 A157993 * A355707 A115175 A104949

Adjacent sequences: A175744 A175745 A175746 * A175748 A175749 A175750

Keyword

nonn

Author

Jaroslav Krizek, Aug 27 2010

Extensions

Extended by T. D. Noe, May 08 2011

Status

approved