cp's OEIS Frontend

A137485 Numbers with 22 divisors.

%I A137485 #22 Feb 22 2025 01:23:01
%S A137485 3072,5120,7168,11264,13312,17408,19456,23552,29696,31744,37888,41984,
%T A137485 44032,48128,54272,60416,62464,68608,72704,74752,80896,84992,91136,
%U A137485 99328,103424,105472,109568,111616,115712,118098,130048,134144,140288
%N A137485 Numbers with 22 divisors.
%C A137485 Maple implementation: see A030513.
%C A137485 Numbers of the form p^21 or p*q^10, where p and q are distinct primes. - _R. J. Mathar_, Mar 01 2010
%H A137485 T. D. Noe, <a href="/A137485/b137485.txt">Table of n, a(n) for n = 1..1000</a>
%F A137485 A000005(a(n))=22.
%p A137485 A137485=proc(q) local n;
%p A137485 for n from 1 to q do if tau(n)=22 then print(n); fi; od; end:
%p A137485 A137485(10^10);
%t A137485 Select[Range[200000],DivisorSigma[0,#]==22&] (* _Vladimir Joseph Stephan Orlovsky_, May 05 2011 *)
%o A137485 (PARI) is(n)=numdiv(n)==22 \\ _Charles R Greathouse IV_, Jun 19 2016
%o A137485 (Python)
%o A137485 from sympy import primepi, integer_nthroot, primerange
%o A137485 def A137485(n):
%o A137485     def bisection(f,kmin=0,kmax=1):
%o A137485         while f(kmax) > kmax: kmax <<= 1
%o A137485         kmin = kmax >> 1
%o A137485         while kmax-kmin > 1:
%o A137485             kmid = kmax+kmin>>1
%o A137485             if f(kmid) <= kmid:
%o A137485                 kmax = kmid
%o A137485             else:
%o A137485                 kmin = kmid
%o A137485         return kmax
%o A137485     def f(x): return n+x-sum(primepi(x//p**10) for p in primerange(integer_nthroot(x,10)[0]+1))+primepi(integer_nthroot(x,11)[0])-primepi(integer_nthroot(x,21)[0])
%o A137485     return bisection(f,n,n) # _Chai Wah Wu_, Feb 21 2025
%Y A137485 Cf. A030513-A030516, A030626, A030627, A030634-A030638, A005179, A003680, A096932, A061286, A061283.
%K A137485 nonn
%O A137485 1,1
%A A137485 _R. J. Mathar_, Apr 22 2008