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A175747 Numbers with 38 divisors.

%I A175747 #24 Feb 22 2025 12:19:54
%S A175747 786432,1310720,1835008,2883584,3407872,4456448,4980736,6029312,
%T A175747 7602176,8126464,9699328,10747904,11272192,12320768,13893632,15466496,
%U A175747 15990784,17563648,18612224,19136512,20709376,21757952,23330816,25427968,26476544,27000832,28049408
%N A175747 Numbers with 38 divisors.
%C A175747 Numbers of the forms p^37 and p^18*q^1, where p and q are distinct primes.
%H A175747 T. D. Noe, <a href="/A175747/b175747.txt">Table of n, a(n) for n = 1..1000</a>
%H A175747 OEIS Wiki, <a href="https://oeis.org/wiki/Index_entries_for_number_of_divisors">Index entries for number of divisors</a>
%F A175747 A000005(a(n))=38.
%t A175747 Select[Range[10000000],DivisorSigma[0,#]==38&] (* _Vladimir Joseph Stephan Orlovsky_, May 06 2011 *)
%o A175747 (PARI) is(n)=numdiv(n)==38 \\ _Charles R Greathouse IV_, Jun 19 2016
%o A175747 (Python)
%o A175747 def A175747(n):
%o A175747     def bisection(f,kmin=0,kmax=1):
%o A175747         while f(kmax) > kmax: kmax <<= 1
%o A175747         kmin = kmax >> 1
%o A175747         while kmax-kmin > 1:
%o A175747             kmid = kmax+kmin>>1
%o A175747             if f(kmid) <= kmid:
%o A175747                 kmax = kmid
%o A175747             else:
%o A175747                 kmin = kmid
%o A175747         return kmax
%o A175747     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]))
%o A175747     return bisection(f,n,n) # _Chai Wah Wu_, Feb 22 2025
%Y A175747 Cf. A175745, A175746, A139572.
%K A175747 nonn
%O A175747 1,1
%A A175747 _Jaroslav Krizek_, Aug 27 2010
%E A175747 Extended by _T. D. Noe_, May 08 2011