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A168352 Products of 6 distinct odd primes.

%I A168352 #24 Sep 10 2024 20:19:42
%S A168352 255255,285285,345345,373065,435435,440895,451605,465465,504735,
%T A168352 533715,555555,569415,596505,608685,615615,636405,645645,672945,
%U A168352 680295,692835,705705,719355,726495,752115,770385,780045,795795,803985,805035,811965,823515,838695,844305,858585
%N A168352 Products of 6 distinct odd primes.
%H A168352 David A. Corneth, <a href="/A168352/b168352.txt">Table of n, a(n) for n = 1..10000</a>
%F A168352 A067885 INTERSECT A005408. [_R. J. Mathar_, Nov 24 2009]
%e A168352 255255 = 3*5*7*11*13*17
%e A168352 285285 = 3*5*7*11*13*19
%e A168352 345345 = 3*5*7*11*13*23
%e A168352 435435 = 3*5*7*11*13*29
%t A168352 f[n_]:=Last/@FactorInteger[n]=={1,1,1,1,1,1}&&FactorInteger[n][[1,1]]>2; lst={};Do[If[f[n],AppendTo[lst,n]],{n,6*9!}];lst
%o A168352 (PARI) is(n) = {n%2 == 1 && factor(n)[,2]~ == [1,1,1,1,1,1]} \\ _David A. Corneth_, Aug 26 2020
%o A168352 (Python)
%o A168352 from sympy import primefactors, factorint
%o A168352 print([n for n in range(1, 1000000, 2) if len(primefactors(n)) == 6 and max(list(factorint(n).values())) == 1]) # _Karl-Heinz Hofmann_, Mar 01 2023
%o A168352 (Python)
%o A168352 from math import prod, isqrt
%o A168352 from sympy import primerange, integer_nthroot, primepi
%o A168352 def A168352(n):
%o A168352     def g(x,a,b,c,m): yield from (((d,) for d in enumerate(primerange(b+1,isqrt(x//c)+1),a+1)) if m==2 else (((a2,b2),)+d for a2,b2 in enumerate(primerange(b+1,integer_nthroot(x//c,m)[0]+1),a+1) for d in g(x,a2,b2,c*b2,m-1)))
%o A168352     def f(x): return int(n+x-sum(primepi(x//prod(c[1] for c in a))-a[-1][0] for a in g(x,1,2,1,6)))
%o A168352     def bisection(f, kmin=0, kmax=1):
%o A168352         while f(kmax) > kmax: kmax <<= 1
%o A168352         while kmax-kmin > 1:
%o A168352             kmid = kmax+kmin>>1
%o A168352             if f(kmid) <= kmid:
%o A168352                 kmax = kmid
%o A168352             else:
%o A168352                 kmin = kmid
%o A168352         return kmax
%o A168352     return bisection(f,n,n) # _Chai Wah Wu_, Sep 10 2024
%Y A168352 Cf. A005408, A067885.
%Y A168352 Cf. A046391 (5 distinct odd primes).
%K A168352 nonn,easy
%O A168352 1,1
%A A168352 _Vladimir Joseph Stephan Orlovsky_, Nov 23 2009
%E A168352 Definition corrected by _R. J. Mathar_, Nov 24 2009
%E A168352 More terms from _David A. Corneth_, Aug 26 2020