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 A062090 a(1) = 1, a(n) = smallest odd number that does not divide the product of all previous terms. 13
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 22 07:57 EDT 2023. Contains 365519 sequences. (Running on oeis4.)