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

1,2

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

Links

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

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Odd terms of {1} U A050376.

Subsequence of A336882.

Sequence in context: A080429 A326581 A050150 * A358975 A345898 A172095

Adjacent sequences: A062087 A062088 A062089 * A062091 A062092 A062093

Keyword

nonn,easy,nice

Author

Amarnath Murthy, Jun 16 2001

Extensions

Corrected and extended by Dean Hickerson, Jul 10 2001

Status

approved