%I #20 Jul 29 2021 16:26:14

%S 1,3,5,7,9,11,13,17,19,23,25,29,31,37,41,43,47,49,53,59,61,67,71,73,

%T 79,81,83,89,97,101,103,107,109,113,121,127,131,137,139,149,151,157,

%U 163,167,169,173,179,181,191,193,197,199,211,223,227,229,233,239,241

%N a(1) = 1, a(n) = smallest odd number that does not divide the product of all previous terms.

%C In A050150 but not here: [729, 15625, 59049, 117649, 531441]; here but not in A050150: [1, 6561, 390625]. - _Klaus Brockhaus_, Nov 01 2001

%C If "a(1) = 1," is removed from the definition, the subsequent terms remain the same, since 1 is the empty product. The resulting sequence then comprises the odd terms of A050376. - _Peter Munn_, Nov 03 2020

%H T. D. Noe, <a href="/A062090/b062090.txt">Table of n, a(n) for n=1..1000</a>

%F 1 together with numbers of the form p^(2^k) where p is an odd prime and k is a nonnegative integer. [Corrected by _Peter Munn_, Nov 03 2020]

%F For n >= 2, a(n) = A336882(2^(n-2)). - _Peter Munn_, Nov 03 2020

%e After 13 the next term is 17 (not 15) as 15 = 3*5 divides the product of all the previous terms.

%t a = {1}; Do[b = Apply[ Times, a]; k = 1; While[ IntegerQ[b/k], k += 2]; a = Append[a, k], { n, 2, 60} ]; a

%t nxt[{p_,on_}]:=Module[{c=on+2},While[Divisible[p,c],c+=2];{p*c,c}]; NestList[ nxt,{1,1},60][[All,2]] (* _Harvey P. Dale_, Jul 29 2021 *)

%o (Haskell)

%o a062090 n = a062090_list !! (n-1)

%o a062090_list = f [1, 3 ..] [] where

%o f (x:xs) ys = g x ys where

%o g _ [] = x : f xs (x : ys)

%o g 1 _ = f xs ys

%o g z (v:vs) = g (z `div` gcd z v) vs

%o -- _Reinhard Zumkeller_, Aug 16 2013

%Y Cf. A026477, A062091, A050150 (a different sequence).

%Y Odd terms of {1} U A050376.

%Y Subsequence of A336882.

%K nonn,easy,nice

%O 1,2

%A _Amarnath Murthy_, Jun 16 2001

%E Corrected and extended by _Dean Hickerson_, Jul 10 2001