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%I #34 Jun 22 2021 03:01:38
%S 1,2,3,5,7,11,15,22,30,42,56,77,101,135,176,231,297,303,385,405,490,
%T 505,528,539,627,675,693,707,792,880,891,945,1002,1155,1232,1255,1485,
%U 1617,1925,1936,2079,2450,2541,2695,3135,3267,3430,3465,3960,4235
%N Incrementally largest number of nonisomorphic finite Abelian groups as a function of order.
%C Records in A000688. - _Artur Jasinski_, Mar 14 2008
%H Amiram Eldar, <a href="/A046054/b046054.txt">Table of n, a(n) for n = 1..1111</a> (terms 1..216 from Charlie Neder)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AbelianGroup.html">Abelian Group</a>
%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F a(n) = A000688(A046055(n)). - _Amiram Eldar_, Aug 20 2019
%t a = {}; b = 0; f[n_] := Times @@ PartitionsP /@ Last /@ FactorInteger@n; k = Array[f, 1000000]; Do[If[k[[m]] > b, b = k[[m]]; AppendTo[a, b]], {m, 1, Length[k]}]; a (* using a procedure from _Robert G. Wilson v_; _Artur Jasinski_, Mar 14 2008 *)
%Y Cf. A000688, A046055, A046056.
%K nonn
%O 1,2
%A _Eric W. Weisstein_
%E More terms from _David Wasserman_, Feb 06 2002
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