%I #13 Sep 02 2020 23:06:17

%S 1,1,5,95,8823,4952323,20285515801,714092378624317

%N Number of strict chains of divisors in A130091 (numbers with distinct prime multiplicities) starting with the superprimorial A006939(n) and ending with 1.

%F a(n) = A336423(A006939(n)) = A336571(A006939(n)).

%e The a(0) = 1 through a(2) = 5 chains:

%e {1} {2,1} {12,1}

%e {12,2,1}

%e {12,3,1}

%e {12,4,1}

%e {12,4,2,1}

%t chern[n_]:=Product[Prime[i]^(n-i+1),{i,n}];

%t chnstr[n_]:=If[n==1,1,Sum[chnstr[d],{d,Select[Most[Divisors[n]],UnsameQ@@Last/@FactorInteger[#]&]}]];

%t Table[chnstr[chern[n]],{n,0,3}]

%Y A076954 can be used instead of A006939 (cf. A307895, A325337).

%Y A336423 and A336571 are not restricted to A006939.

%Y A336941 is the version not restricted by A130091.

%Y A337075 is the version for factorials.

%Y A074206 counts chains of divisors from n to 1.

%Y A130091 lists numbers with distinct prime multiplicities.

%Y A181796 counts divisors with distinct prime multiplicities.

%Y A253249 counts chains of divisors.

%Y A327498 gives the maximum divisor with distinct prime multiplicities.

%Y A336422 counts divisible pairs of divisors, both in A130091.

%Y A336424 counts factorizations using A130091.

%Y Cf. A000005, A001055, A002033, A032741, A067824, A124010, A167865, A336419, A336420, A336500, A336568.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Aug 14 2020