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 A123073 #9 Oct 20 2024 12:38:51 %S A123073 1,3,3,3,1,3,6,6,3,3,3,3,3,6,3,6,3,3,6,3,3,3,6,6,6,6,3,3,3,1,6,6,3,3, %T A123073 3,6,3,6,6,3,3,6,3,6,6,3,6,6,3,3,6,6,6,3,6,3,3,3,6,6,6,3,6,3,6,3,3,6, %U A123073 3,6,6,6,3,6,3,6,6,3,3,3,3,1,6,6,3,6,3,6,3,6,6,6,3,3,6,6,3,6,6,3,6,3,3,6,3 %N A123073 Number of ordered triples of primes (p,q,r) such that pqr = n-th 3-almost prime A014612(n). %C A123073 The nonzero subsequence of A123074. %o A123073 (Python) %o A123073 from math import isqrt %o A123073 from sympy import primepi, primerange, integer_nthroot, primefactors %o A123073 def A123073(n): %o A123073 def bisection(f,kmin=0,kmax=1): %o A123073 while f(kmax) > kmax: kmax <<= 1 %o A123073 while kmax-kmin > 1: %o A123073 kmid = kmax+kmin>>1 %o A123073 if f(kmid) <= kmid: %o A123073 kmax = kmid %o A123073 else: %o A123073 kmin = kmid %o A123073 return kmax %o A123073 def f(x): return int(n+x-sum(primepi(x//(k*m))-b for a,k in enumerate(primerange(integer_nthroot(x,3)[0]+1)) for b,m in enumerate(primerange(k,isqrt(x//k)+1),a))) %o A123073 return (1,3,6)[len(primefactors(bisection(f,n,n)))-1] # _Chai Wah Wu_, Oct 20 2024 %Y A123073 Cf. A123074, A014612. %K A123073 nonn %O A123073 1,2 %A A123073 _N. J. A. Sloane_ and T. D. Noe, Sep 29 2006 %E A123073 More terms from _T. D. Noe_, Sep 29 2006