cp's OEIS Frontend

A343939 Number of n-chains of divisors of n.

%I A343939 #6 May 06 2021 21:24:41
%S A343939 1,3,4,15,6,49,8,165,55,121,12,1183,14,225,256,4845,18,3610,20,4851,
%T A343939 484,529,24,73125,351,729,4060,12615,30,29791,32,435897,1156,1225,
%U A343939 1296,494209,38,1521,1600,505981,42,79507,44,46575,49726,2209,48
%N A343939 Number of n-chains of divisors of n.
%e A343939 The a(1) = 1 through a(5) = 6 chains:
%e A343939   (1)  (1/1)  (1/1/1)  (1/1/1/1)  (1/1/1/1/1)
%e A343939        (2/1)  (3/1/1)  (2/1/1/1)  (5/1/1/1/1)
%e A343939        (2/2)  (3/3/1)  (2/2/1/1)  (5/5/1/1/1)
%e A343939               (3/3/3)  (2/2/2/1)  (5/5/5/1/1)
%e A343939                        (2/2/2/2)  (5/5/5/5/1)
%e A343939                        (4/1/1/1)  (5/5/5/5/5)
%e A343939                        (4/2/1/1)
%e A343939                        (4/2/2/1)
%e A343939                        (4/2/2/2)
%e A343939                        (4/4/1/1)
%e A343939                        (4/4/2/1)
%e A343939                        (4/4/2/2)
%e A343939                        (4/4/4/1)
%e A343939                        (4/4/4/2)
%e A343939                        (4/4/4/4)
%t A343939 Table[Length[Select[Tuples[Divisors[n],n],OrderedQ[#]&&And@@Divisible@@@Reverse/@Partition[#,2,1]&]],{n,10}]
%Y A343939 Diagonal n = k - 1 of the array A077592.
%Y A343939 Chains of length n - 1 are counted by A163767.
%Y A343939 Diagonal n = k of the array A334997.
%Y A343939 The version counting all multisets of divisors (not just chains) is A343935.
%Y A343939 A000005(n) counts divisors of n.
%Y A343939 A067824(n) counts strict chains of divisors starting with n.
%Y A343939 A074206(n) counts strict chains of divisors from n to 1.
%Y A343939 A146291(n,k) counts divisors of n with k prime factors (with multiplicity).
%Y A343939 A251683(n,k-1) counts strict k-chains of divisors from n to 1.
%Y A343939 A253249(n) counts nonempty chains of divisors of n.
%Y A343939 A334996(n,k) counts strict k-chains of divisors from n to 1.
%Y A343939 A337255(n,k) counts strict k-chains of divisors starting with n.
%Y A343939 A343658(n,k) counts k-multisets of divisors of n.
%Y A343939 A343662(n,k) counts strict k-chains of divisors of n (row sums: A337256).
%Y A343939 Cf. A062319, A066959, A143773, A176029, A327527, A343656.
%K A343939 nonn
%O A343939 1,2
%A A343939 _Gus Wiseman_, May 05 2021