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a(1) = 2, a(n)= smallest even number which does not divide the product of all previous terms.
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%I #11 Nov 07 2020 11:36:06

%S 2,4,6,10,14,18,22,26,34,38,46,50,58,62,74,82,86,94,98,106,118,122,

%T 134,142,146,158,162,166,178,194,202,206,214,218,226,242,254,262,274,

%U 278,298,302,314,326,334,338,346,358,362,382,386,394,398,422,446,454

%N a(1) = 2, a(n)= smallest even number which does not divide the product of all previous terms.

%H Michael De Vlieger, <a href="/A062091/b062091.txt">Table of n, a(n) for n = 1..10000</a>

%F 2 and 4 together with numbers of the form 2*{p^(2^k)} where p is an odd prime and k is a nonnegative integer. [Corrected by _Peter Munn_, Nov 03 2020]

%e After 10 the next term in the sequence is 14 (not 12) as 12 = 2*6 divides the product of all the previous terms.

%t Block[{a = {2}, k = 4, P = 1}, Do[Set[P, P*a[[-1]]]; While[Mod[P, k] == 0, k += 2]; AppendTo[a, k], {i, 2, 56}]; a] (* _Michael De Vlieger_, Nov 04 2020 *)

%Y Cf. A026477, A062090.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Jun 16 2001

%E More terms from _Dean Hickerson_, Jul 10 2001