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 A343662 #7 May 01 2021 21:55:36
%S A343662 1,1,1,2,1,1,2,1,1,3,3,1,1,2,1,1,4,5,2,1,2,1,1,4,6,4,1,1,3,3,1,1,4,5,
%T A343662 2,1,2,1,1,6,12,10,3,1,2,1,1,4,5,2,1,4,5,2,1,5,10,10,5,1,1,2,1,1,6,12,
%U A343662 10,3,1,2,1,1,6,12,10,3,1,4,5,2,1,4,5,2
%N A343662 Irregular triangle read by rows where T(n,k) is the number of strict length k chains of divisors of n, 0 <= k <= Omega(n) + 1.
%e A343662 Triangle begins:
%e A343662 1: 1 1
%e A343662 2: 1 2 1
%e A343662 3: 1 2 1
%e A343662 4: 1 3 3 1
%e A343662 5: 1 2 1
%e A343662 6: 1 4 5 2
%e A343662 7: 1 2 1
%e A343662 8: 1 4 6 4 1
%e A343662 9: 1 3 3 1
%e A343662 10: 1 4 5 2
%e A343662 11: 1 2 1
%e A343662 12: 1 6 12 10 3
%e A343662 13: 1 2 1
%e A343662 14: 1 4 5 2
%e A343662 15: 1 4 5 2
%e A343662 16: 1 5 10 10 5 1
%e A343662 For example, row n = 12 counts the following chains:
%e A343662 () (1) (2/1) (4/2/1) (12/4/2/1)
%e A343662 (2) (3/1) (6/2/1) (12/6/2/1)
%e A343662 (3) (4/1) (6/3/1) (12/6/3/1)
%e A343662 (4) (4/2) (12/2/1)
%e A343662 (6) (6/1) (12/3/1)
%e A343662 (12) (6/2) (12/4/1)
%e A343662 (6/3) (12/4/2)
%e A343662 (12/1) (12/6/1)
%e A343662 (12/2) (12/6/2)
%e A343662 (12/3) (12/6/3)
%e A343662 (12/4)
%e A343662 (12/6)
%t A343662 Table[Length[Select[Reverse/@Subsets[Divisors[n],{k}],And@@Divisible@@@Partition[#,2,1]&]],{n,15},{k,0,PrimeOmega[n]+1}]
%Y A343662 Column k = 1 is A000005.
%Y A343662 Row ends are A008480.
%Y A343662 Row lengths are A073093.
%Y A343662 Column k = 2 is A238952.
%Y A343662 The case from n to 1 is A334996 or A251683 (row sums: A074206).
%Y A343662 A non-strict version is A334997 (transpose: A077592).
%Y A343662 The case starting with n is A337255 (row sums: A067824).
%Y A343662 Row sums are A337256 (nonempty: A253249).
%Y A343662 A001055 counts factorizations.
%Y A343662 A001221 counts distinct prime factors.
%Y A343662 A001222 counts prime factors with multiplicity.
%Y A343662 A097805 counts compositions by sum and length.
%Y A343662 A122651 counts strict chains of divisors summing to n.
%Y A343662 A146291 counts divisors of n with k prime factors (with multiplicity).
%Y A343662 A163767 counts length n - 1 chains of divisors of n.
%Y A343662 A167865 counts strict chains of divisors > 1 summing to n.
%Y A343662 A337070 counts strict chains of divisors starting with superprimorials.
%Y A343662 Cf. A002033, A007425, A007426, A051026, A062319, A143773, A186972, A327527, A337074, A337105, A337107, A343658.
%K A343662 nonn,tabf
%O A343662 1,4
%A A343662 _Gus Wiseman_, May 01 2021