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A238985 Zeroless 7-smooth numbers.

%I A238985 #40 Jan 28 2023 10:34:33
%S A238985 1,2,3,4,5,6,7,8,9,12,14,15,16,18,21,24,25,27,28,32,35,36,42,45,48,49,
%T A238985 54,56,63,64,72,75,81,84,96,98,112,125,126,128,135,144,147,162,168,
%U A238985 175,189,192,196,216,224,225,243,245,252,256,288,294,315,324,336
%N A238985 Zeroless 7-smooth numbers.
%C A238985 A001221(a(n)) <= 3 since 10 cannot divide a(n).
%C A238985 It seems that this sequence is finite and contains 12615 terms. - _Daniel Mondot_, May 03 2022 and _Jianing Song_, Jan 28 2023
%H A238985 Daniel Mondot, <a href="/A238985/b238985.txt">Table of n, a(n) for n = 1..12615</a> (terms 1..10000 from Charles R Greathouse IV)
%F A238985 A086299(a(n)) * A168046(a(n)) = 1.
%e A238985 a(12615) = 2^25 * 3^227 * 7^28.
%o A238985 (Haskell)
%o A238985 import Data.Set (singleton, deleteFindMin, fromList, union)
%o A238985 a238985 n = a238985_list !! (n-1)
%o A238985 a238985_list = filter ((== 1) . a168046) $ f $ singleton 1 where
%o A238985    f s = x : f (s' `union` fromList
%o A238985                (filter ((> 0) . (`mod` 10)) $ map (* x) [2,3,5,7]))
%o A238985                where (x, s') = deleteFindMin s
%o A238985 (PARI) zf(n)=vecmin(digits(n))
%o A238985 list(lim)=my(v=List(),t,t1); for(e=0,log(lim+1)\log(7), t1=7^e; for(f=0,log(lim\t1+1)\log(3), t=t1*3^f; while(t<=lim, if(zf(t), listput(v, t)); t<<=1)); for(f=0,log(lim\t1+1)\log(5), t=t1*5^f; while(t<=lim, if(zf(t), listput(v, t)); t*=3))); Set(v)
%Y A238985 Cf. A168046, intersection of A002473 and A052382.
%Y A238985 A238938, A238939, A238940, A195948, A238936, A195908 are proper subsequences.
%Y A238985 Cf. A059405 (subsequence), A350180 through A350187.
%K A238985 nonn,base
%O A238985 1,2
%A A238985 _Charles R Greathouse IV_ and _Reinhard Zumkeller_, Mar 07 2014
%E A238985 Keyword:fini and keyword:full removed by _Jianing Song_, Jan 28 2023 as finiteness is only conjectured.