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 A271654 #19 Dec 03 2023 12:31:10
%S A271654 1,2,2,5,2,17,2,44,30,137,2,695,2,1731,1094,6907,2,30653,2,97244,
%T A271654 38952,352739,2,1632933,10628,5200327,1562602,20357264,2,87716708,2,
%U A271654 303174298,64512738,1166803145,1391282,4978661179,2,17672631939,2707475853,69150651910,2,286754260229,2,1053966829029,115133177854,4116715363847,2,16892899722499,12271514,63207357886437
%N A271654 a(n) = Sum_{k|n} binomial(n-1,k-1).
%C A271654 Also the number of compositions of n whose length divides n, i.e., compositions with integer mean, ranked by A096199. - _Gus Wiseman_, Sep 28 2022
%H A271654 Alois P. Heinz, <a href="/A271654/b271654.txt">Table of n, a(n) for n = 1..3329</a>
%e A271654 From _Gus Wiseman_, Sep 28 2022: (Start)
%e A271654 The a(1) = 1 through a(6) = 17 compositions with integer mean:
%e A271654 (1) (2) (3) (4) (5) (6)
%e A271654 (1,1) (1,1,1) (1,3) (1,1,1,1,1) (1,5)
%e A271654 (2,2) (2,4)
%e A271654 (3,1) (3,3)
%e A271654 (1,1,1,1) (4,2)
%e A271654 (5,1)
%e A271654 (1,1,4)
%e A271654 (1,2,3)
%e A271654 (1,3,2)
%e A271654 (1,4,1)
%e A271654 (2,1,3)
%e A271654 (2,2,2)
%e A271654 (2,3,1)
%e A271654 (3,1,2)
%e A271654 (3,2,1)
%e A271654 (4,1,1)
%e A271654 (1,1,1,1,1,1)
%e A271654 (End)
%p A271654 a:= n-> add(binomial(n-1, d-1), d=numtheory[divisors](n)):
%p A271654 seq(a(n), n=1..50); # _Alois P. Heinz_, Dec 03 2023
%t A271654 Table[Length[Join @@ Permutations/@Select[IntegerPartitions[n],IntegerQ[Mean[#]]&]],{n,15}] (* _Gus Wiseman_, Sep 28 2022 *)
%o A271654 (PARI) a(n)=sumdiv(n,k,binomial(n-1,k-1))
%Y A271654 Cf. A056045.
%Y A271654 The version for nonempty subsets is A051293, geometric A326027.
%Y A271654 The version for partitions is A067538, ranked by A316413, strict A102627.
%Y A271654 These compositions are ranked by A096199.
%Y A271654 The version for factorizations is A326622, geometric A326028.
%Y A271654 A011782 counts compositions.
%Y A271654 A067539 = partitions w integer geo mean, ranked by A326623, strict A326625.
%Y A271654 A100346 counts compositions into divisors, partitions A018818.
%Y A271654 Cf. A000041, A078174, A078175, A326567/A326568, A326624, A326641, A326836, A326837, A326843.
%K A271654 nonn
%O A271654 1,2
%A A271654 _Franklin T. Adams-Watters_, Apr 11 2016