This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A328966 #4 Nov 16 2019 20:04:28 %S A328966 1,1,1,1,1,1,2,1,1,1,2,1,1,2,2,1,1,1,2,2,1,1,4,1,1,2,2,1,1,1,3,2,1,2, %T A328966 2,1,1,2,3,1,2,1,2,3,1,1,5,1,1,2,2,1,1,2,3,2,1,1,5,1,1,3,3,2,1,1,2,2, %U A328966 1,1,5,1,1,3,2,2,2,1,5,2,1,1,4,2,1,2,3 %N A328966 Number of strict factorizations of n with integer average. %e A328966 The a(n) factorizations for n = 2, 8, 24, 48, 96: %e A328966 (2) (8) (24) (32) (48) (96) %e A328966 (2*4) (4*6) (4*8) (6*8) (2*48) %e A328966 (2*12) (2*16) (2*24) (4*24) %e A328966 (2*3*4) (4*12) (6*16) %e A328966 (2*4*6) (8*12) %e A328966 (3*4*8) %e A328966 (2*3*16) %e A328966 (2*4*12) %t A328966 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]]; %t A328966 Table[Length[Select[facs[n],UnsameQ@@#&&IntegerQ[Mean[#]]&]],{n,2,100}] %Y A328966 The non-strict version is A326622. %Y A328966 Partitions with integer average are A067538. %Y A328966 Strict partitions with integer average are A102627. %Y A328966 Heinz numbers of partitions with integer average are A316413. %Y A328966 Factorizations with integer geometric mean are A326028. %Y A328966 Cf. A001055, A051293, A078174, A078175, A326515, A326567/A326568, A326619/A326620, A326621, A326625. %K A328966 nonn %O A328966 2,7 %A A328966 _Gus Wiseman_, Nov 16 2019