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%I #11 Mar 11 2023 17:36:09
%S 8,96,480,1440,40320,443520,1330560,34594560,86486400,588107520,
%T 1470268800,11174042880,55870214400,195545750400,1285014931200,
%U 17990209036800,53970627110400,1565148186201600,194078375088998400,7180899878292940800,35904499391464704000,294416895010010572800
%N Numbers disqualified from being in A019505 for not being the smallest number with their respective number of divisors.
%C It appears that when 2*A019505(n) is a member of this sequence then the exponent in at least one primary of the factorization of A019505(n+1) is smaller than in the corresponding primary of A019505(n) or A019505(n+1) contains an additional prime factor. The smallest example in this sequence where two primaries have smaller exponents and an additional prime factor is added is a(14) = 2*A019505(43) = 2 * 97772875200 = 195545750400. The sequence of exponents of its primaries is (7, 3, 2, 2, 1, 1, 1, 1 ) while A019505(44) = 160626866400 has exponent sequence (5, 3, 2, 1, 1, 1, 1, 1, 1 ). - _Hartmut F. W. Hoft_, Feb 22 2023
%e 8 qualifies because 8 = 4*2 and 4 is in A019505, but 8 can't be term after 4 in A019505 because smallest number with 4 divisors is 6.
%t dataA019505 = Map[Last, Import[URL["https://oeis.org/A019505/b019505.txt"], "Data"]]
%t dataA241813 = Take[Map[First, Select[Map[{2#[[1]], 2#[[1]]==#[[2]]}&, Transpose[{Most[dataA019505], Rest[dataA019505]}]], !#[[2]]&]], 22] (* _Hartmut F. W. Hoft_, Feb 22 2023 *)
%Y Cf. A019505, A140635.
%K nonn,more
%O 1,1
%A _J. Lowell_, Apr 29 2014
%E More terms from _Hartmut F. W. Hoft_, Feb 22 2023
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