This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A289173 #41 Apr 22 2025 04:33:55
%S A289173 2,6,20,60,208,624,2080,6240,18720,58240,176000,529408,1593344,
%T A289173 4780032,14344192,43040768,129138688,387416064,1162248192,3486777344,
%U A289173 10460332032,31380996096,94142988288,282428964864,847286894592,2541860683776,7625582051328
%N A289173 The largest n-almost prime less than 3^n.
%C A289173 All terms are even as 3^n is the first odd n-almost prime.
%H A289173 Jon E. Schoenfield, <a href="/A289173/b289173.txt">Table of n, a(n) for n = 1..100</a>
%e A289173 a(26) = 2541860683776 = 3^26 - 5144553 = 2^18*3^6*47*283 (a 26-almost prime).
%e A289173 From _Michael De Vlieger_, Jun 27 2017: (Start)
%e A289173 Table of prime factors of a(n) for 1 <= n <= 16:
%e A289173 1: 2
%e A289173 2: 2 3
%e A289173 3: 2 2 5
%e A289173 4: 2 2 3 5
%e A289173 5: 2 2 2 2 13
%e A289173 6: 2 2 2 2 3 13
%e A289173 7: 2 2 2 2 2 5 13
%e A289173 8: 2 2 2 2 2 3 5 13
%e A289173 9: 2 2 2 2 2 3 3 5 13
%e A289173 10: 2 2 2 2 2 2 2 5 7 13
%e A289173 11: 2 2 2 2 2 2 2 5 5 5 11
%e A289173 12: 2 2 2 2 2 2 2 2 2 2 11 47
%e A289173 13: 2 2 2 2 2 2 2 2 2 2 2 2 389
%e A289173 14: 2 2 2 2 2 2 2 2 2 2 2 2 3 389
%e A289173 15: 2 2 2 2 2 2 2 2 2 2 2 2 2 17 103
%e A289173 16: 2 2 2 2 2 2 2 2 2 2 2 2 2 2 37 71(End)
%t A289173 Table[SelectFirst[Range[3^n - 1, 2^n, -1], PrimeOmega@ # == n &], {n, 18}] (* _Michael De Vlieger_, Jun 27 2017 *)
%o A289173 (PARI) for (n = 1,26, m = 3^n-1; while(bigomega(m) <> n, m = m-2); print1 (m ","))
%o A289173 (PARI) a(n)=my(target=n-1); forstep(k=3^n\2,1,-1, if(bigomega(k)==target, return(2*k))) \\ _Charles R Greathouse IV_, Jul 05 2017
%o A289173 (Python)
%o A289173 from math import prod, isqrt
%o A289173 from sympy import primepi, primerange, integer_nthroot
%o A289173 def A289173(n):
%o A289173 def bisection(f,kmin=0,kmax=1):
%o A289173 while f(kmax) > kmax: kmax <<= 1
%o A289173 kmin = kmax >> 1
%o A289173 while kmax-kmin > 1:
%o A289173 kmid = kmax+kmin>>1
%o A289173 if f(kmid) <= kmid:
%o A289173 kmax = kmid
%o A289173 else:
%o A289173 kmin = kmid
%o A289173 return kmax
%o A289173 def almostprimepi(n,k):
%o A289173 if k==0: return int(n>=1)
%o A289173 def g(x,a,b,c,m): yield from (((d,) for d in enumerate(primerange(b,isqrt(x//c)+1),a)) if m==2 else (((a2,b2),)+d for a2,b2 in enumerate(primerange(b,integer_nthroot(x//c,m)[0]+1),a) for d in g(x,a2,b2,c*b2,m-1)))
%o A289173 return int(sum(primepi(n//prod(c[1] for c in a))-a[-1][0] for a in g(n,0,1,1,k)) if k>1 else primepi(n))
%o A289173 m = almostprimepi(3**n-1,n)
%o A289173 def f(x): return m+x-almostprimepi(x,n)
%o A289173 return bisection(f,m,m) # _Chai Wah Wu_, Mar 29 2025
%Y A289173 Cf. A078843 (where 3^n occurs in n-almost primes).
%K A289173 nonn
%O A289173 1,1
%A A289173 _Zak Seidov_, Jun 26 2017
%E A289173 a(27) from _Jon E. Schoenfield_, Jul 02 2017