%I #24 Feb 22 2025 01:22:57
%S 576,1600,2916,3136,7744,10816,18225,18496,23104,33856,35721,53824,
%T 61504,62500,87616,88209,107584,118336,123201,140625,141376,179776,
%U 210681,222784,238144,263169,287296,322624,341056,385641,399424,440896
%N Numbers with 21 divisors.
%C Maple implementation: see A030513.
%C Numbers of the form p^20 or p^2*q^6 (A189990) where p and q are distinct primes. - _R. J. Mathar_, Mar 01 2010
%H T. D. Noe, <a href="/A137484/b137484.txt">Table of n, a(n) for n = 1..1000</a>
%F A000005(a(n)) = 21.
%F Sum_{n>=1} 1/a(n) = P(2)*P(6) - P(8) + P(20) = 0.00365945..., where P is the prime zeta function. - _Amiram Eldar_, Jul 03 2022
%t Select[Range[450000],DivisorSigma[0,#]==21&] (* _Vladimir Joseph Stephan Orlovsky_, May 03 2011 *)
%o (PARI) is(n)=numdiv(n)==21 \\ _Charles R Greathouse IV_, Jun 19 2016
%o (Python)
%o from math import isqrt
%o from sympy import primepi, primerange, integer_nthroot
%o def A137484(n):
%o def bisection(f,kmin=0,kmax=1):
%o while f(kmax) > kmax: kmax <<= 1
%o kmin = kmax >> 1
%o while kmax-kmin > 1:
%o kmid = kmax+kmin>>1
%o if f(kmid) <= kmid:
%o kmax = kmid
%o else:
%o kmin = kmid
%o return kmax
%o def f(x): return n+x-sum(primepi(isqrt(x//p**6)) for p in primerange(integer_nthroot(x,6)[0]+1))+primepi(integer_nthroot(x,8)[0])-primepi(integer_nthroot(x,20)[0])
%o return bisection(f,n,n) # _Chai Wah Wu_, Feb 21 2025
%Y Cf. A000005, A030513, A030638 (20 divisors), A137485 (22 divisors), A189990.
%K nonn,changed
%O 1,1
%A _R. J. Mathar_, Apr 22 2008