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 A179672 #30 Apr 22 2025 04:12:43
%S A179672 960,1344,2112,2240,2496,3264,3520,3648,4160,4416,4928,5440,5568,5824,
%T A179672 5952,6080,7104,7290,7360,7616,7872,8256,8512,9024,9152,9280,9920,
%U A179672 10176,10206,10304,11328,11712,11840,11968,12864,12992,13120,13376,13632
%N A179672 Products of the 6th power of a prime and 2 distinct primes (p^6*q*r).
%H A179672 T. D. Noe, <a href="/A179672/b179672.txt">Table of n, a(n) for n = 1..1000</a>
%H A179672 Will Nicholes, <a href="https://willnicholes.com/2010/06/06/list-of-prime-signatures">List of Prime Signatures</a>
%H A179672 <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>
%t A179672 f[n_]:=Sort[Last/@FactorInteger[n]]=={1,1,6}; Select[Range[20000], f]
%o A179672 (PARI) list(lim)=my(v=List(),t1,t2);forprime(p=2, (lim\6)^(1/6), t1=p^6;forprime(q=2, lim\t1, if(p==q, next);t2=t1*q;forprime(r=q+1, lim\t2, if(p==r,next);listput(v,t2*r)))); vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jul 20 2011
%o A179672 (Python)
%o A179672 from math import isqrt
%o A179672 from sympy import primepi, primerange, integer_nthroot
%o A179672 def A179672(n):
%o A179672 def bisection(f,kmin=0,kmax=1):
%o A179672 while f(kmax) > kmax: kmax <<= 1
%o A179672 kmin = kmax >> 1
%o A179672 while kmax-kmin > 1:
%o A179672 kmid = kmax+kmin>>1
%o A179672 if f(kmid) <= kmid:
%o A179672 kmax = kmid
%o A179672 else:
%o A179672 kmin = kmid
%o A179672 return kmax
%o A179672 def f(x): return n+x+sum((t:=primepi(s:=isqrt(y:=x//r**6)))+(t*(t-1)>>1)-sum(primepi(y//k) for k in primerange(1, s+1)) for r in primerange(integer_nthroot(x,6)[0]+1))+sum(primepi(x//p**7) for p in primerange(integer_nthroot(x,7)[0]+1))-primepi(integer_nthroot(x,8)[0])
%o A179672 return bisection(f,n,n) # _Chai Wah Wu_, Mar 27 2025
%K A179672 nonn
%O A179672 1,1
%A A179672 _Vladimir Joseph Stephan Orlovsky_, Jul 23 2010