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

1, 3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241

Offset: 1

Author

Amarnath Murthy, Jun 16 2001

Keywords

• nonn
• easy
• nice

Comments

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

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

Examples

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

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Crossrefs

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

Odd terms of {1} U A050376.

Subsequence of A336882.

Programs

Haskell

a062090 n = a062090_list !! (n-1)
a062090_list = f [1, 3 ..] [] where
   f (x:xs) ys = g x ys where
     g _ []     = x : f xs (x : ys)
     g 1 _      = f xs ys
     g z (v:vs) = g (z `div` gcd z v) vs
-- Reinhard Zumkeller, Aug 16 2013

Mathematica

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

Formula

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]

For n >= 2, a(n) = A336882(2^(n-2)). - Peter Munn, Nov 03 2020

Extensions

Corrected and extended by Dean Hickerson, Jul 10 2001