A238985 Zeroless 7-smooth numbers.

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, 54, 56, 63, 64, 72, 75, 81, 84, 96, 98, 112, 125, 126, 128, 135, 144, 147, 162, 168, 175, 189, 192, 196, 216, 224, 225, 243, 245, 252, 256, 288, 294, 315, 324, 336

Offset: 1

Author

Charles R Greathouse IV and Reinhard Zumkeller, Mar 07 2014

Keywords

• nonn
• base

Comments

A001221(a(n)) <= 3 since 10 cannot divide a(n).

It seems that this sequence is finite and contains 12615 terms. - Daniel Mondot, May 03 2022 and Jianing Song, Jan 28 2023

Examples

			a(12615) = 2^25 * 3^227 * 7^28.
		

Links

• Daniel Mondot, Table of n, a(n) for n = 1..12615 (terms 1..10000 from Charles R Greathouse IV)

Crossrefs

Cf. A168046, intersection of A002473 and A052382.

A238938, A238939, A238940, A195948, A238936, A195908 are proper subsequences.

Cf. A059405 (subsequence), A350180 through A350187.

Programs

Haskell

import Data.Set (singleton, deleteFindMin, fromList, union)
a238985 n = a238985_list !! (n-1)
a238985_list = filter ((== 1) . a168046) $ f $ singleton 1 where
   f s = x : f (s' `union` fromList
               (filter ((> 0) . (`mod` 10)) $ map (* x) [2,3,5,7]))
               where (x, s') = deleteFindMin s

PARI

zf(n)=vecmin(digits(n))
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)

Formula

A086299(a(n)) * A168046(a(n)) = 1.

Extensions

Keyword:fini and keyword:full removed by Jianing Song, Jan 28 2023 as finiteness is only conjectured.