A046054 Incrementally largest number of nonisomorphic finite Abelian groups as a function of order.

1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 303, 385, 405, 490, 505, 528, 539, 627, 675, 693, 707, 792, 880, 891, 945, 1002, 1155, 1232, 1255, 1485, 1617, 1925, 1936, 2079, 2450, 2541, 2695, 3135, 3267, 3430, 3465, 3960, 4235

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Comments

Records in A000688. - Artur Jasinski, Mar 14 2008

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1111 (terms 1..216 from Charlie Neder)
• Eric Weisstein's World of Mathematics, Abelian Group
• Index entries for sequences related to groups

Crossrefs

Cf. A000688, A046055, A046056.

Programs

Mathematica

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 *)

Formula

a(n) = A000688(A046055(n)). - Amiram Eldar, Aug 20 2019

Extensions

More terms from David Wasserman, Feb 06 2002