A337070 - OEIS

%I #12 Sep 02 2020 23:06:29

%S 1,2,16,1208,1383936,32718467072,20166949856488576,

%T 391322675415566237681536

%N Number of strict chains of divisors starting with the superprimorial A006939(n).

%C The n-th superprimorial is A006939(n) = Product_{i = 1..n} prime(i)^(n - i + 1).

%F a(n) = 2*A336941(n) for n > 0.

%F a(n) = A067824(A006939(n)).

%e The a(0) = 1 through a(2) = 16 chains:

%e   1  2    12

%e      2/1  12/1

%e           12/2

%e           12/3

%e           12/4

%e           12/6

%e           12/2/1

%e           12/3/1

%e           12/4/1

%e           12/4/2

%e           12/6/1

%e           12/6/2

%e           12/6/3

%e           12/4/2/1

%e           12/6/2/1

%e           12/6/3/1

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

%t chnsc[n_]:=If[n==1,{{1}},Prepend[Join@@Table[Prepend[#,n]&/@chnsc[d],{d,Most[Divisors[n]]}],{n}]];

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

%Y A022915 is the maximal case.

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

%Y A336571 is the case with distinct prime multiplicities.

%Y A336941 is the case ending with 1.

%Y A337071 is the version for factorials.

%Y A000005 counts divisors.

%Y A000142 counts divisors of superprimorials.

%Y A006939 lists superprimorials or Chernoff numbers.

%Y A067824 counts chains of divisors starting with n.

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

%Y A253249 counts chains of divisors.

%Y A317829 counts factorizations of superprimorials.

%Y Cf. A001055, A002033, A167865, A181818, A336420, A336423, A336942, A337074.

%K nonn,more

%O 0,2

%A _Gus Wiseman_, Aug 15 2020