cp's OEIS Frontend

A062090 a(1) = 1, a(n) = smallest odd number that does not divide the product of all previous terms.

%I A062090 #20 Jul 29 2021 16:26:14
%S A062090 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 A062090 79,81,83,89,97,101,103,107,109,113,121,127,131,137,139,149,151,157,
%U A062090 163,167,169,173,179,181,191,193,197,199,211,223,227,229,233,239,241
%N A062090 a(1) = 1, a(n) = smallest odd number that does not divide the product of all previous terms.
%C A062090 In A050150 but not here: [729, 15625, 59049, 117649, 531441]; here but not in A050150: [1, 6561, 390625]. - _Klaus Brockhaus_, Nov 01 2001
%C A062090 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 A062090 T. D. Noe, <a href="/A062090/b062090.txt">Table of n, a(n) for n=1..1000</a>
%F A062090 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 A062090 For n >= 2, a(n) = A336882(2^(n-2)). - _Peter Munn_, Nov 03 2020
%e A062090 After 13 the next term is 17 (not 15) as 15 = 3*5 divides the product of all the previous terms.
%t A062090 a = {1}; Do[b = Apply[ Times, a]; k = 1; While[ IntegerQ[b/k], k += 2]; a = Append[a, k], { n, 2, 60} ]; a
%t A062090 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 A062090 (Haskell)
%o A062090 a062090 n = a062090_list !! (n-1)
%o A062090 a062090_list = f [1, 3 ..] [] where
%o A062090    f (x:xs) ys = g x ys where
%o A062090      g _ []     = x : f xs (x : ys)
%o A062090      g 1 _      = f xs ys
%o A062090      g z (v:vs) = g (z `div` gcd z v) vs
%o A062090 -- _Reinhard Zumkeller_, Aug 16 2013
%Y A062090 Cf. A026477, A062091, A050150 (a different sequence).
%Y A062090 Odd terms of {1} U A050376.
%Y A062090 Subsequence of A336882.
%K A062090 nonn,easy,nice
%O A062090 1,2
%A A062090 _Amarnath Murthy_, Jun 16 2001
%E A062090 Corrected and extended by _Dean Hickerson_, Jul 10 2001