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

1,2

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

Links

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

Formula

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

Example

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

Prog

(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)

Crossrefs

Cf. A168046, intersection of A002473 and A052382.

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

Cf. A059405 (subsequence), A350180 through A350187.

Sequence in context: A350572 A290387 A342950 * A337230 A226900 A111228

Adjacent sequences: A238982 A238983 A238984 * A238986 A238987 A238988

Keyword

nonn,base

Author

Charles R Greathouse IV and Reinhard Zumkeller, Mar 07 2014

Extensions

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

Status

approved